Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators

Linear Algebra and Its Applications

Volumn 381, Issue 1-3, 2004, Pages 219-235

  Furuta, Takayuki ^a  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

Operator concave function; Reverse type Shannon inequality; Shannon inequality

Indexed keywords

ESTIMATION; FUNCTIONS; MATHEMATICAL OPERATORS; PROBABILITY; THEOREM PROVING; VECTORS;

OPERATOR CONCAVE FUNCTION; REVERSE TYPE SHANNON INEQUALITY; SHANNON INEQUALITY;

LINEAR ALGEBRA;

EID: 1342306715     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2003.11.017     Document Type: Article

References (10)

1. P.S. Bullen, A dictionary of inequalities, Pitman Monographs and Surveys in Pure and Applied Mathematics 97, Addison Wesley Longman, 1998.
2. Fujii J.I., Kamei E. Relative operator entropy in noncommutative information theory. Math. Japonica. 34:1989;341-348.
3. Fujii J.I., Kamei E. Uhlmann's interpolational method for operator means. Math. Japonica. 34:1989;541-547.
4. Hansen F. An operator inequality. Math. Ann. 246:1980;249-250.
5. Hansen F., Pedersen G.K. Jensen's inequality for operators and Löwner theorem. Math. Ann. 258:1982;229-241.
6. Kwong M.K. Some results on matrix monotone functions. Linear Algebra Appl. 118:1989;129-153.
7. Kullback S., Leibler R.A. On information and sufficiency. Ann. Math. Stat. 22:1951;79-86.
8. Nakamura M., Umegaki H. A note on the entropy for operator algebra. Proc. Jpn. Acad. 37:1961;149-154.
9. Shannon C.E. A mathematical theory of communication. Bull. Syst. Tech. J. 27:1948;379-423. 623-656.
10. Hansen F., Pedersem G.K. Jensen's operator inequality. Bull. Lond. Math. Soc. 35:2003;553-564.