BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES

We obtain a generalization of Buzano’s inequality of vectors in Hilbert spaces , using the theory of algebraic probability spaces. In particular, we extend a result of Dragomir given in [7]. Applications for numerical inequalities for n- tuples of bounded linear operators and functions of operators...

Full description

Autores:: Agredo, J.
Leon, Y.
Osorio, J.
Peña, A.

Tipo de recurso:: Article of investigation

Fecha de publicación:: 2019

Institución:: Escuela Colombiana de Ingeniería Julio Garavito

Repositorio:: Repositorio Institucional ECI

Idioma:: eng

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dc.title.eng.fl_str_mv	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
title	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
spellingShingle	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES Buzano’s inequality Algebraic probability spaces Desigualdad de Buzano Espacios algebraicos de probabilidad.
title_short	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
title_full	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
title_fullStr	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
title_full_unstemmed	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
title_sort	BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
dc.creator.fl_str_mv	Agredo, J. Leon, Y. Osorio, J. Peña, A.
dc.contributor.author.none.fl_str_mv	Agredo, J. Leon, Y. Osorio, J. Peña, A.
dc.contributor.researchgroup.spa.fl_str_mv	Matemáticas
dc.subject.proposal.eng.fl_str_mv	Buzano’s inequality Algebraic probability spaces
topic	Buzano’s inequality Algebraic probability spaces Desigualdad de Buzano Espacios algebraicos de probabilidad.
dc.subject.proposal.spa.fl_str_mv	Desigualdad de Buzano Espacios algebraicos de probabilidad.
description	We obtain a generalization of Buzano’s inequality of vectors in Hilbert spaces , using the theory of algebraic probability spaces. In particular, we extend a result of Dragomir given in [7]. Applications for numerical inequalities for n- tuples of bounded linear operators and functions of operators defined by double power series are also generalized.
publishDate	2019
dc.date.available.none.fl_str_mv	2019 2021-10-01T17:20:50Z
dc.date.issued.none.fl_str_mv	2019
dc.date.accessioned.none.fl_str_mv	2021-05-05T04:59:28Z 2021-10-01T17:20:50Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.identifier.uri.none.fl_str_mv	https://repositorio.escuelaing.edu.co/handle/001/1391
dc.identifier.doi.none.fl_str_mv	10.7153/jmi-2019-13-38
dc.identifier.url.none.fl_str_mv	https://dx.doi.org/10.7153/jmi-2019-13-38
identifier_str_mv	1846579X 10.7153/jmi-2019-13-38
url	https://repositorio.escuelaing.edu.co/handle/001/1391 https://dx.doi.org/10.7153/jmi-2019-13-38
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.citationedition.spa.fl_str_mv	Journal of Mathematical Inequalities ISSN: 1846-579X, 2019 vol:13 fasc: 2 págs: 585 - 599
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dc.relation.citationstartpage.spa.fl_str_mv	585
dc.relation.citationvolume.spa.fl_str_mv	13
dc.relation.indexed.spa.fl_str_mv	N/A
dc.relation.ispartofjournal.spa.fl_str_mv	Journal of Mathematical Inequalities
dc.relation.references.eng.fl_str_mv	J. AGREDO, F. FAGNOLA, R. REBOLLEDO, Decoherence free subspaces of a quantum Markov semigroup, J. Math. Phys., 55, 112201 (2014). S. ATTAL, Elements of Operators Algebras and Modular Theory, Open Quantum Systems I: The Hamiltonian approach, Springer Verlag, Lectures Notes in Mathematics, 2006, 1–105. O. BRATELLI, D. W. ROBINSON, Operator Algebras and Quantum Statistical Mechanics, SpringerVerlag 1, 1987. M. L. BUZANO, Generalizzazione della diseguaglianza di Cauchy–Schwartz, Rend. Sem. Mat. Univ. e Politech. Torino, 31, (1974), 405–409 A. CONNES, Noncommutative Geometry, Academic Press, 1994 F. D’ANDREA, Pythagoras Theorem in Noncommutative Geometry, Proceedings of the Conference on Optimal Transport and Noncommutative Geometry, Besancon 2014, Available at arXiv:1507.08773. S. S. DRAGOMIR, Generalizations of Buzano inequality for n -tuples of vectors in inner product spaces with applications, Tbilisi Mathematical Journal, 10, 2 (2017), 29–41. S. S. DRAGOMIR, M. KHOSRAVI, M. S. MOSLEHIAN, Bessel type inequalities in Hilbert modules, Linear Multilinear Algebra, 58, 8 (2010), 967–975 S. S. DRAGOMIR, Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Tamkang J. Math., 39, 1 (2008), 1–7. S. S. DRAGOMIR, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Demostratio Math., 40, 2 (2007), 411–417. S. S. DRAGOMIR, A potpourri of Schwarz related inequalities in inner product spaces (II), J. Inequal. Pure Appl. Math.; 7, 1 (2006), Article 14. S. S. DRAGOMIR, I. SANDOR ´ , Some inequalities in pre-Hilbertian spaces, Studia Univ. Babes-Bolyai Math., 32, 1 (1987), 71–78. S. S. DRAGOMIR, Some refinements of Schwartz inequality, Simpozionul de Matematici si Aplicatii, Timisoaria, Romania, 1-2 Noiembrie, (1985), 13–16. F. FAGNOLA, V. UMANIT‘A, Generic quantum Markov semigroups, cycle decomposition and deviation from equilibrium, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 15, 3 (2012), 1–17. F. FAGNOLA, R. REBOLLEDO, Algebraic conditions for convergence of a quantum Markov semigroup to a steady state, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 11, 3 (2008), 467–474. F. FAGNOLA, R. REBOLLEDO, Subharmonic projections for a quantum Markov semigroup, J. Math. Phys., 43, 2 (2002). F. FAGNOLA, Quantum Markov semigroups and quantum Markov flows, Proyecciones., 18, 3 (1999), 1–144. J. I. FUJII, M. FUJII, M. S. MOSLEHIAN, J. E. PECARIC, Y. SEO, Reverses Cauchy-Schwarz type inequalities in pre-inner product C∗ -modules, Hokkaido Math. J., 40, (2011), 1–17. M. FUJII, Operator-valued inner product and operator inequalities, Banach J. Math. Anal., 2, 2 (2008), 59–67. M. FUJII, F. KUBO, Buzano’s inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc., 117, (1993), 359–361. D. ILISEVIC, S. VAROSANEC, On the Cauchy-Schwarz inequality and its reverse in semi-inner product C∗ -modules, Banach J. Math. Anal., 1, (2007), 78–84. M. S. MOSLEHIAN, L. - E. PERSSON, Reverse Cauchy-Schwarz inequalities for positive C∗ -valued sesquilinear forms, Math. Inequal. Appl., 4, 12, (2009), 701–709. A. HORA, N. OBATA, Quantum Probability and Spectral Analysis of Graphs, Series: Theoretical and Mathematical Physics, Springer, Berlin Heidelberg, 2007. K. R. PARTHASARATHY, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics 85, 1992. U. RICHARD, Sur des in´egalit´es du type Wirtinger et leurs application aux ´equationes diff´erentielles ordinaires, Colloquium of Analysis held in Rio de Janeiro, (1972), 233–244. W. RUDIN, Real and complex analysis, McGraw-Hill, 1987. S. SALIMI,Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory, Quantum Information Processing, 9, 1 (2010), 75–91. S. SALIMI, Quantum Central Limit Theorem for Continuous-Time Quantum Walks on Odd Graphs in Quantum Probability Theory, International Journal of Theoretical Physics, 47, 12, (2008), 3298–3309. S. SALIMI, Study of continuous-time quantum walks on quotient graphs via quantum probability theory, International Journal of Quantum Information, 6, 4, (2008), 945–957. K. TANAHASHI, A. UCHIYAMA, M. UCHIYAMA, On Schwarz type inequalities, Proc. Amer. Math. Soc., 131, 8, (2003) 2549–2552. M. TAKESAKI, Theory of operator algebras I, Springer-Verlag New York Heidelberg, 1979.
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spelling	Agredo, J.24ae437804d29d9ce505e3ca85b7b763600Leon, Y.f5269de41fae2680f55240defca17f68600Osorio, J.6ae52c9ca4b9f2b889994625d46af904600Peña, A.f1c028110a8eb53ecab93e384d7d1e0b600Matemáticas2021-05-05T04:59:28Z2021-10-01T17:20:50Z20192021-10-01T17:20:50Z20191846579Xhttps://repositorio.escuelaing.edu.co/handle/001/139110.7153/jmi-2019-13-38https://dx.doi.org/10.7153/jmi-2019-13-38We obtain a generalization of Buzano’s inequality of vectors in Hilbert spaces , using the theory of algebraic probability spaces. In particular, we extend a result of Dragomir given in [7]. Applications for numerical inequalities for n- tuples of bounded linear operators and functions of operators defined by double power series are also generalized.Obtenemos una generalización de la desigualdad de Buzano de vectores en espacios de Hilbert , utilizando la teoría de los espacios algebraicos de probabilidad. En particular, extendemos un resultado de Dragomir dado en [7]. Aplicaciones para desigualdades numéricas para n-tuplas de operadores lineales acotados y funciones de operadores definidos por series de potencias dobles también se generalizan. Traducción realizada con la versión gratuita del traductor www.DeepL.com/TranslatorAcknowledgement. The authors want to highlight the support from Escuela colombiana de ingenier´ıa “Julio Garavito”.J. Agredo Department of Mathematics Colombian School of Engineering “Julio Garavito” Bogot´a, Colombia e-mail: julian.agredo@escuelaing.edu.coY. Leon Department of Mathematics Colombian School of Engineering “Julio Garavito” Bogot´a, Colombia e-mail: yessica.leon@mail.escuelaing.edu.coJ. Osorio Department of Mathematics Colombian School of Engineering “Julio Garavito” Bogot´a, Colombia e-mail: juan.osorio-r@mail.escuelaing.edu.coA. Pe˜na Department of Mathematics Colombian School of Engineering “Julio Garavito” Bogot´a, Colombia e-mail: alvaro.pena-m@mail.escuelaing.edu.co15 páginasapplication/pdfenghttp://files.ele-math.com/articles/jmi-13-38.pdfBUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACESArtículo de revistainfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85CroaciaJournal of Mathematical Inequalities ISSN: 1846-579X, 2019 vol:13 fasc: 2 págs: 585 - 599599258513N/AJournal of Mathematical InequalitiesJ. AGREDO, F. FAGNOLA, R. REBOLLEDO, Decoherence free subspaces of a quantum Markov semigroup, J. Math. Phys., 55, 112201 (2014).S. ATTAL, Elements of Operators Algebras and Modular Theory, Open Quantum Systems I: The Hamiltonian approach, Springer Verlag, Lectures Notes in Mathematics, 2006, 1–105.O. BRATELLI, D. W. ROBINSON, Operator Algebras and Quantum Statistical Mechanics, SpringerVerlag 1, 1987.M. L. BUZANO, Generalizzazione della diseguaglianza di Cauchy–Schwartz, Rend. Sem. Mat. Univ. e Politech. Torino, 31, (1974), 405–409A. CONNES, Noncommutative Geometry, Academic Press, 1994F. D’ANDREA, Pythagoras Theorem in Noncommutative Geometry, Proceedings of the Conference on Optimal Transport and Noncommutative Geometry, Besancon 2014, Available at arXiv:1507.08773.S. S. DRAGOMIR, Generalizations of Buzano inequality for n -tuples of vectors in inner product spaces with applications, Tbilisi Mathematical Journal, 10, 2 (2017), 29–41.S. S. DRAGOMIR, M. KHOSRAVI, M. S. MOSLEHIAN, Bessel type inequalities in Hilbert modules, Linear Multilinear Algebra, 58, 8 (2010), 967–975S. S. DRAGOMIR, Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Tamkang J. Math., 39, 1 (2008), 1–7.S. S. DRAGOMIR, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Demostratio Math., 40, 2 (2007), 411–417.S. S. DRAGOMIR, A potpourri of Schwarz related inequalities in inner product spaces (II), J. Inequal. Pure Appl. Math.; 7, 1 (2006), Article 14.S. S. DRAGOMIR, I. SANDOR ´ , Some inequalities in pre-Hilbertian spaces, Studia Univ. Babes-Bolyai Math., 32, 1 (1987), 71–78.S. S. DRAGOMIR, Some refinements of Schwartz inequality, Simpozionul de Matematici si Aplicatii, Timisoaria, Romania, 1-2 Noiembrie, (1985), 13–16.F. FAGNOLA, V. UMANIT‘A, Generic quantum Markov semigroups, cycle decomposition and deviation from equilibrium, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 15, 3 (2012), 1–17.F. FAGNOLA, R. REBOLLEDO, Algebraic conditions for convergence of a quantum Markov semigroup to a steady state, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 11, 3 (2008), 467–474.F. FAGNOLA, R. REBOLLEDO, Subharmonic projections for a quantum Markov semigroup, J. Math. Phys., 43, 2 (2002).F. FAGNOLA, Quantum Markov semigroups and quantum Markov flows, Proyecciones., 18, 3 (1999), 1–144.J. I. FUJII, M. FUJII, M. S. MOSLEHIAN, J. E. PECARIC, Y. SEO, Reverses Cauchy-Schwarz type inequalities in pre-inner product C∗ -modules, Hokkaido Math. J., 40, (2011), 1–17.M. FUJII, Operator-valued inner product and operator inequalities, Banach J. Math. Anal., 2, 2 (2008), 59–67.M. FUJII, F. KUBO, Buzano’s inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc., 117, (1993), 359–361.D. ILISEVIC, S. VAROSANEC, On the Cauchy-Schwarz inequality and its reverse in semi-inner product C∗ -modules, Banach J. Math. Anal., 1, (2007), 78–84.M. S. MOSLEHIAN, L. - E. PERSSON, Reverse Cauchy-Schwarz inequalities for positive C∗ -valued sesquilinear forms, Math. Inequal. Appl., 4, 12, (2009), 701–709.A. HORA, N. OBATA, Quantum Probability and Spectral Analysis of Graphs, Series: Theoretical and Mathematical Physics, Springer, Berlin Heidelberg, 2007.K. R. PARTHASARATHY, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics 85, 1992.U. RICHARD, Sur des in´egalit´es du type Wirtinger et leurs application aux ´equationes diff´erentielles ordinaires, Colloquium of Analysis held in Rio de Janeiro, (1972), 233–244.W. RUDIN, Real and complex analysis, McGraw-Hill, 1987.S. SALIMI,Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory, Quantum Information Processing, 9, 1 (2010), 75–91.S. SALIMI, Quantum Central Limit Theorem for Continuous-Time Quantum Walks on Odd Graphs in Quantum Probability Theory, International Journal of Theoretical Physics, 47, 12, (2008), 3298–3309.S. SALIMI, Study of continuous-time quantum walks on quotient graphs via quantum probability theory, International Journal of Quantum Information, 6, 4, (2008), 945–957.K. TANAHASHI, A. UCHIYAMA, M. UCHIYAMA, On Schwarz type inequalities, Proc. Amer. Math. Soc., 131, 8, (2003) 2549–2552.M. 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BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES

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