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BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES

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Agredo, J.
Leon, Y.
Osorio, J.
Peña, A.
Abstract (Spanish)
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/Translator
Abstract (English)
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.
Extent
15 páginas
URI: https://repositorio.escuelaing.edu.co/handle/001/1391
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AC - GIMATH: Grupo de investigación en Matemáticas de la Escuela Colombiana de Ingeniería
References

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.