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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the equivalence of multiplicity and the generalized topological degree


Authors: T. O’Neil and J. W. Thomas
Journal: Trans. Amer. Math. Soc. 167 (1972), 333-345
MSC: Primary 47H10; Secondary 58E05
MathSciNet review: 0298503
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Abstract: In this paper we first extend the definition of the multiplicity (as defined by J. Cronin-Scanlon) of operators of the form $ I + C + T$ to operators of the form $ H + C + T$. We then show that the generalized topological degree (as defined by F. E. Browder and W. V. Petryshyn) of operators of the form $ H + C + T$ is also defined. Finally, we show that when both the multiplicity and generalized topological degree of $ H + C + T$ are defined, they are equal.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0298503-3
PII: S 0002-9947(1972)0298503-3
Keywords: Topological degree, generalized topological degree, multiplicity of an operator, compact mappings, A-proper mappings
Article copyright: © Copyright 1972 American Mathematical Society