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ArticleOriginal scientific text

Title

Almost exactness in normed spaces II

Authors 1, 2, 3, 4

Affiliations

  1. School of Mathematics, Trinity College, Dublin, Ireland
  2. Instituto de Matemáticas, Universidad Nacional, Autónoma de México, México 04510 DF, Mexico
  3. Université des Sciences et Technologies de Lille, U.R.A. D 751 CNRS "GAT", U.F.R. de Mathématiques, F-59655 Villeneuve d'ascq Cedex France
  4. University of Galatasaray, Ciragan Acd. No: 102, Ortakoy 80840, Istanbul, Turkey

Abstract

In the normed space of bounded operators between a pair of normed spaces, the set of operators which are "bounded below" forms the interior of the set of one-one operators. This note is concerned with the extension of this observation to certain spaces of pairs of operators.

Bibliography

  1. R. E. Harte, Almost open mappings between normed spaces, Proc. Amer. Math. Soc. 90 (1984), 243-249.
  2. R. E. Harte, Almost exactness in normed spaces, ibid. 100 (1987), 257-265.
  3. R. E. Harte, Invertibility and Singularity, Dekker, New York, 1988.
  4. R. E. Harte, Taylor exactness and Kato's jump, Proc. Amer. Math. Soc. 119 (1993), 793-801.
  5. M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105.
  6. F. A. Potra and V. Pták, Nondiscrete Induction and Iterative Processes, Pitman Res. Notes 103, Pitman, New York, 1984.
  7. V. Wrobel, The boundary of Taylor's joint spectrum for a pair of commuting Banach space operators, Studia Math. 84 (1986), 105-111.
Studia Mathematica
1995-1996/117/2
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Pages:
101-105
Main language of publication
English
Received
1992-04-30
Accepted
1995-06-14
Published
1996
Exact and natural sciences