Description

• Title:
  Operator subadditivity of the D-logarithmic integral transform for positive operators in Hilbert spaces
• Creator:
  Dragomir, Silvestru Sever
• Description:
  For a continuous and positive function w(λ), λ>0 and μ a positive measure on [0,∞) we consider the following D-logarithmic integral transformDLog(w,μ)(T) :=∫0∞w(λ)ln(\frac{λ+T}{λ})dμ(λ),where the integral is assumed to exist for T a positive operator on a complex Hilbert space H. We show among others that, if A, B>0 with BA+AB ≥ 0, thenDLog(w,μ)(A) +DLog(w,μ)(B) ≥ DLog(w,μ)(A+B).In particular we have\frac{1}{6}π2+dilog(A+B) ≥ dilog(A) + dilog(B),where the dilogarithmic function dilog : [0,∞)→ℝ is defined bydilog(t) :=∫1t\frac{ln s}{1-s}ds, t ≥ 0.Some examples for integral transform DLog(·,·) related to the operator monotone functions are also provided.
• Object availability:
  free access
• Date:
  2021.05.26
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 35 No 2 (2021); 158-171;
  Annales Mathematicae Silesianae; Tom 35 Nr 2 (2021); 158-171;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13443/10408
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13443
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other