Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An internal characterization of inessential operators


Author: Pietro Aiena
Journal: Proc. Amer. Math. Soc. 102 (1988), 625-626
MSC: Primary 47B05
DOI: https://doi.org/10.1090/S0002-9939-1988-0928992-7
MathSciNet review: 928992
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the ideal of inessential operators $ I(E)$ on a complex Banach space $ E$ as the largest ideal of the class $ \mathcal{A}(E)$ of all bounded linear operators $ A$ having the property that the restrictions $ A\left\vert M \right.$ of $ A$ on any closed infinite-dimensional invariant subspace $ M$ may be.


References [Enhancements On Off] (What's this?)

  • [1] S. Caradus, W. E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators in Banach spaces, Dekker, New York, 1974. MR 0415345 (54:3434)
  • [2] H. Heuser, Functional analysis, Wiley, New York, 1982. MR 640429 (83m:46001)
  • [3] D. Kleinecke, Almost finite, compact and inessential operators, Proc. Amer. Math. Soc. 14 (1963), 863-868. MR 0155197 (27:5136)
  • [4] A. Pietsch, Inessential operators in Banach spaces, Integral Equations Operator Theory 1 (1978), 588-591. MR 516770 (80c:47023)
  • [5] M. Schechter, Riesz operators and Fredholm perturbations, Bull. Amer. Math. Soc. 74 (1968), 1139-1144. MR 0231222 (37:6777)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05

Retrieve articles in all journals with MSC: 47B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0928992-7
Keywords: Inessential and Riesz operators
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society