Gateaux derivative of norm

Author:
Dragoljub J. Kecki\`c

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2061-2067

MSC (2000):
Primary 46G05, 47L05; Secondary 47A30

Published electronically:
January 25, 2005

MathSciNet review:
2137872

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for Hilbert space operators and , it follows that

where . Using the concept of -Gateaux derivative, we apply this result to characterize orthogonality in the sense of James in , and to give an easy proof of the characterization of smooth points in .

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Additional Information

**Dragoljub J. Kecki\`c**

Affiliation:
Faculty of Mathematics, University of Belgrade, Studentski trg 16–18, 11000 Beograd, Serbia & Montenegro

Email:
keckic@matf.bg.ac.yu, keckic@EUnet.yu

DOI:
https://doi.org/10.1090/S0002-9939-05-07746-4

Keywords:
Gateaux derivative,
orthogonality,
smoothness

Received by editor(s):
February 3, 2004

Received by editor(s) in revised form:
March 7, 2004

Published electronically:
January 25, 2005

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.