Generalized Shannon inequalities based on Tsallis relative operator entropy

Linear Algebra and Its Applications

Volumn 394, Issue 1-3, 2005, Pages 109-118

  Yanagi, Kenjiro ^a   Kuriyama, Ken ^a   Furuichi, Shigeru ^b  

^a YAMAGUCHI UNIVERSITY   (Japan)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

Operator inequality; Shannon inequality; Tsallis relative operator entropy

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; LINEAR ALGEBRA; MATHEMATICAL OPERATORS; NUMBER THEORY; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY; STATISTICAL METHODS;

OPERATOR INEQUALITY; QUANTUM SYSTEM; SHANNON INEQUALITY; TSALLIS RELATIVE OPERATOR ENTROPY;

ENTROPY;

EID: 7544220309     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.06.025     Document Type: Article

References (8)

1. S. Abe, Monotonic decrease of the quantum nonadditive divergence by projective measurements, Phys. Lett. A 312 (2003) 336-338.
2. N. Bebiano, J. da Providencia Jr., R. Lemos, Matrix inequalities in statistical mechanics, Linear Algebra Appl. 376 (2004) 265-273.
3. J.I. Fujii, E. Kamei, Relative operator entropy in noncommutative information theory, Math. Japon. 34 (1989) 341-348.
4. T. Furuta, Parametric extensions of Shannon inequality and its reverse one in Hubert space operators, Linear Algebra Appl. 381 (2004) 219-235.
5. F. Hiai, D. Petz, The Golden-Thompson trace inequality is complemented, Linear Algebra Appl. 181 (1993)153-185.
6. C. Tsallis, Possible generalization of Boltzman-Gibbs statistics, J. Statist. Phys. 52 (1988) 479-487.
7. C. Tsallis et al., in: S. Abe, Y. Okamoto (Eds.), Nonextensive Statistical Mechanics and Its Applications, Springer-Verlag, Heidelberg, 2001, Comprehensive list of references available from: 〈http://tsallis.cat.cbpf.br/biblio.htm〉.
8. H. Umegaki, Conditional expectation in an operator algebra, IV (entropy and information), Kodai Math. Sem. Rep. 14 (1962) 59-85.