Vol. 82, No. 2, 1979

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ISSN: 0030-8730
Graph-dense linear transformations

George Golightly

Vol. 82 (1979), No. 2, 371–377
Abstract

This paper extends a decomposition process of [Richard Arens, Operational calculus of linear relations, Pacific J. Math., 11 (1961), 9–23] for closed linear relations, T, on a Hilbert space to the setting in which T is a linear function from a dense linear subspace of a separable normed linear complete space S1 to an innear product space S2. This decomposition is used in showing that such a function contracted to a suitable dense linear subspace of its initial set is the contraction of a closed linear function from a dense linear subspace of S1 to S2. In particular, in case the initial set of T is S1, it is shown that the contraction of T to a suitable dense linear subspace of S1 is the contraction of a continuous linear function from S1 to S2.

Mathematical Subject Classification 2000
Primary: 47A05
Milestones
Received: 30 May 1978
Published: 1 June 1979
Authors
George Golightly