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On Riesz operators

Published online by Cambridge University Press:  20 January 2009

J. C. Alexander
Affiliation:
University of Edinburgh, Edinburgh, 1
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In (4) Vala proves a generalization of Schauder's theorem (3) on the compactness of the adjoint of a compact linear operator. The particular case of Vala's result that we shall be concerned with is as follows. Let t1 and t2 be non-zero bounded linear operators on the Banach spaces Y and X respectively, and denote by 1T2 the operator on B(X, Y) defined by

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Alexander, J. C.Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 118.CrossRefGoogle Scholar
(2)Ruston, A. F.Operators with a Fredholm theory, J. London Math. Soc. 29 (1954), 318326.CrossRefGoogle Scholar
(3)Schauder, J.Über lineare, vollstetige Funktionaloperationen,Studia Math. 2 (1930), 183196.CrossRefGoogle Scholar
(4)Vala, K.On compact sets of compact operators, Ann. Acad. Sci. Fenn. Ser. (3) 16 (1966), 131140.Google Scholar
(5)West, T. T.Riesz operators in Banach spaces, Proc. London Math. Soc. (3) 16 (1966), 131140.CrossRefGoogle Scholar
(6)West, T. T.The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737752.CrossRefGoogle Scholar