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On Certain Classes of Bounded Linear Operators

Published online by Cambridge University Press:  20 November 2018

C-S Lin
C-S Lin*
Affiliation:
Queen's University, Kingston, Ontario
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Let T—c be a Fredholm operator, where T is a bounded linear operator on a complex Banach space and c is a scalar, the set of all such scalars is called the Φ-set of T [2] and was studied by many authors. In this connection, the purpose of the present paper is to investigate some classes Φ(V) of all such operators for any subset V of the complex plane.

Let X be a Banach space over the field C of complex numbers with dim Z = ∞, unless otherwise stated, B(X) the Banach algebra of all bounded linear operators and K(X) the closed two-sided ideal of all compact operators on X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 469 - 473
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Caradus, S. R., Operator of Riesz type, Pacifi. J. Math. 18 (1966), 61-71.Google Scholar
2. Gohberg, I. C. and Krein, M. G., The basic propositions on defect numbers, root numbers and indices of linear operators, Trans. Amer. Math. Soc. (2) 13 (1960), 185-265.Google Scholar
3. Kato, T., Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261-322.Google Scholar
4. Schechter, M., Riesz operators and Fredholm perturbations, Bull. Amer. Math. Soc. (6) 74 (1968), 1139-1144.Google Scholar