Mappings of Hilbert-Schmidt type; their applications to eigenfunction expansions and elliptic boundary problems

K. Maurin

Displaying similar documents to “Mappings of Hilbert-Schmidt type; their applications to eigenfunction expansions and elliptic boundary problems”

Continuous selections in Banach spaces

E. Michael (1963)

Studia Mathematica

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Explicit representation of compact linear operators in Banach spaces via polar sets

David E. Edmunds, Jan Lang (2013)

Studia Mathematica

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We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.

Some characterizations of c-paracompact and c-collectionwise normal spaces by continuous selections (I).

Juan Margalef Roig, Enrique Outerelo Domínguez (1980)

Revista Matemática Hispanoamericana

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In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.