The unilateral shift and a norm equality for bounded linear operators
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- by C.-S. Lin PDF
- Proc. Amer. Math. Soc. 127 (1999), 1693-1696 Request permission
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 $S$ and $T$. The invertibility of an operator which is related to the norm equality is discussed. Some new results about the unilateral shift are given.References
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- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- C.-S. Lin, Generalized Daugavet equations and invertible operators on uniformly convex Banach spaces, J. Math. Anal. Appl. 197 (1996), no. 2, 518–528. MR 1372195, DOI 10.1006/jmaa.1996.0036
Additional Information
- C.-S. Lin
- Affiliation: Department of Mathematics, Bishop’s University, Lennoxville, Quebec, Canada J1M 1Z7
- Email: plin@ubishops.ca
- Received by editor(s): October 21, 1996
- Received by editor(s) in revised form: March 3, 1997, and September 4, 1997
- Published electronically: February 10, 1999
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1693-1696
- MSC (1991): Primary 47B05, 47A30, 47A05, 47A12
- DOI: https://doi.org/10.1090/S0002-9939-99-04743-7
- MathSciNet review: 1487321
Dedicated: Dedicated to Professor Yenn Tseng on her retirement.