## Annals of Functional Analysis

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.

## Top downloads over the last seven days

The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spacesAdvance publication (2018)
Approximate amenability and contractibility of hypergroup algebrasAdvance publication (2018)
A fixed point approach to the stability of $\varphi$-morphisms on Hilbert $C^*$-modulesVolume 1, Number 1 (2010)
Completions and balls in Banach spacesVolume 6, Number 1 (2015)
Properties of the slant weighted Toeplitz operatorVolume 2, Number 1 (2011)
• 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: https://projecteuclid.org/afa

### 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

Volume 7, Number 1 (2016)

##### Abstract

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 $\|A\sharp C\|\geq\|B\|$.