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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

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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