The Annals of Functional Analysis (AFA) is published by Duke University Press on behalf of the Tusi Mathematical Research Group.

AFA is a peer-reviewed quarterly electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). AFA normally publishes survey articles and original research papers numbering 16 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.

Advance publication of articles online is available.

  • ISSN: 2008-8752 (electronic)
  • Publisher: Duke University Press
  • Discipline(s): Mathematics
  • Full text available in Euclid: 2010--
  • Access: Articles older than 5 years are open
  • Euclid URL:

Featured bibliometrics

MR Citation Database MCQ (2017): 0.38
JCR (2017) Impact Factor: 0.455
JCR (2017) Five-year Impact Factor: 0.539
JCR (2017) Ranking: 256/309 (Mathematics); 237/252 (Applied Mathematics)
SJR/SCImago Journal Rank (2017): 0.461

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Best Paper Award 2018

Geometric mean and norm Schwarz inequality

Tsuyoshi Ando Volume 7, Number 1 (2016)


Positivity of a $2\times2$ operator matrix $\left[{A\atop B^*}{B\atop C}\right]\geq0$ implies $\sqrt{\|A\|\cdot\|C\|}\geq\|B\|$ for operator norm $\|\cdot\|$. This can be considered as an operator version of the Schwarz inequality. In this situation, for $A,C\geq0$, there is a natural notion of geometric mean $A\sharp C$, for which $\sqrt{\|A\|\cdot\|C\|}\geq\|A\sharp C\|$. In this paper, we study under what conditions on $A$, $B$, and $C$ or on $B$ alone the norm inequality $\sqrt{\|A\|\cdot\|C\|}\geq\|B\|$ can be improved as $\|A\sharp C\|\geq\|B\|$.