Linear Operators: Spectral operators |
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Page 2197
Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ea } be a monotone generalized sequence ( a monotone sequence ) in B. Then , if { Ex } is increasing , lim EX ( V Ed ) , Eg X e X , while ...
Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ea } be a monotone generalized sequence ( a monotone sequence ) in B. Then , if { Ex } is increasing , lim EX ( V Ed ) , Eg X e X , while ...
Page 2218
Let { Ex } be a weakly convergent generalized sequence in B and suppose that its limit E is a projection . It must be shown that { Ea } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E ...
Let { Ex } be a weakly convergent generalized sequence in B and suppose that its limit E is a projection . It must be shown that { Ea } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E ...
Page 2450
By Theorem X.3.4 there exists a complete orthonormal basis { xn } consisting of eigenvectors of T. We let Txn = nXn , and suppose that none of the eigenvalues in is multiple ( that is , that the sequence { n } contains no repetitions ) ...
By Theorem X.3.4 there exists a complete orthonormal basis { xn } consisting of eigenvectors of T. We let Txn = nXn , and suppose that none of the eigenvalues in is multiple ( that is , that the sequence { n } contains no repetitions ) ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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