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An internal characterization of inessential operators

Author: Pietro Aiena
Journal: Proc. Amer. Math. Soc. 102 (1988), 625-626
MSC: Primary 47B05
MathSciNet review: 928992
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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)

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Keywords: Inessential and Riesz operators
Article copyright: © Copyright 1988 American Mathematical Society

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