Douglas Suth Bridges - Locating Ax, where A is a subspace of B(H)

lmcs:962 - Logical Methods in Computer Science, June 16, 2014, Volume 10, Issue 2 -
Locating Ax, where A is a subspace of B(H)

Authors: Douglas Suth Bridges

    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].

    Volume: Volume 10, Issue 2
    Published on: June 16, 2014
    Accepted on: June 25, 2015
    Submitted on: January 4, 2013
    Keywords: Mathematics - Functional Analysis


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