Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The unilateral shift and a norm equality for bounded linear operators

Author(s): C.-S. Lin
Journal: Proc. Amer. Math. Soc. 127 (1999), 1693-1696.
MSC (1991): Primary 47B05, 47A30, 47A05, 47A12
Posted: February 10, 1999
MathSciNet review: 1487321
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Abstract: The paper gives a necessary and sufficient condition for the norm equality $\parallel S-T\parallel =\parallel S\parallel +\parallel T\parallel$ of bounded linear operators and . The invertibility of an operator which is related to the norm equality is discussed. Some new results about the unilateral shift are given.

References:

[1]: Y.A. Abramovich, C.D. Aliprantis, and O. Burkinshaw, The Daugavet equation in uniformly convex Banach spaces, J. Funct. Anal. 97(1991), 215-230. MR 92i:47005
[2]: P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, N.J., 1967. MR 34:8178
[3]: C.-S. Lin, Generalized Daugavet equations and invertible operators on uniformly convex Banach spaces, J. Math. Anal. and Appl. 197(1996),

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Additional Information:

C.-S. Lin
Affiliation: Department of Mathematics, Bishop's University, Lennoxville, Quebec, Canada J1M 1Z7
Email: plin@ubishops.ca

DOI: 10.1090/S0002-9939-99-04743-7
PII: S 0002-9939(99)04743-7
Received by editor(s): October 21, 1996
Received by editor(s) in revised form: March 3, 1997 and September 4, 1997
Posted: February 10, 1999
Dedicated: Dedicated to Professor Yenn Tseng on her retirement.
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1999, American Mathematical Society

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