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arXiv · 1404.6956

Locating Ax, where A is a subspace of B(H)

Douglas Suth Bridges
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Abstract

Let A be a linear space of operators on a Hilbert space H, x a vector in H, and Ax the subspace of H comprising all vectors of the form Tx with T in A. We discuss, within a Bishop-style constructive framework, conditions under which the projection [Ax] of H on the closure of Ax exists. We derive a general result that leads directly to both the open mapping theorem and our main theorem on the existence of [Ax].

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Douglas Suth Bridges. 2014-04-28. Locating Ax, where A is a subspace of B(H). https://doi.org/10.2168/lmcs-10(2:9)2014

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