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Improjective operators and ideals in a category of Banach spaces

Published online by Cambridge University Press:  09 April 2009

E. Tarafdar
E. Tarafdar
Affiliation:
School of Mathematical Sciences, Flinders University, South Australia
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Kato [3] has introduced a class of operators called strictly singular operators. These operators have many properties in common with compact operators. In fact the concept of a strictly singular operator is an extension of the concept of a compact operator. Kato has proved that if X and X′ are Banach Spaces, then the singular operators of X into X′ forms a closed subspace of the space of bounded linear operators of X into X′ and if X = X′, then these operators forms a two-sided ideal in the ring of bounded linear operators on X. He has also shown that the Riers-Schauder theorem holds for the spectrum of a strictly singular operator. Gohberg, Feldman and Markus [23] have treated the same class of operators with an equivalent definition.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 274 - 292
Copyright
Copyright © Australian Mathematical Society 1972

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