Linear Operators, Part 1 |
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Page 481
Let E , and E , be commuting projections in a B - space X. = EzX , N ; = ( I – E ; ) X
, i = 1 , 2 , then ( a ) E , E , = E , if and only if M , CMı , or equivalently , if and only if
N C Nz ; ( b ) if E = E + E , -E , E2 , then E is a projection with EX = sp { M , UM ...
Let E , and E , be commuting projections in a B - space X. = EzX , N ; = ( I – E ; ) X
, i = 1 , 2 , then ( a ) E , E , = E , if and only if M , CMı , or equivalently , if and only if
N C Nz ; ( b ) if E = E + E , -E , E2 , then E is a projection with EX = sp { M , UM ...
Page 482
Thus , the family of all projections in B ( X ) form a partially ordered set . Any two
... We conclude this section with a few remarks on projections in Hilbert space .
Let E be a projection in Hilbert space H , and let E * be its Hilbert space adjoint .
Thus , the family of all projections in B ( X ) form a partially ordered set . Any two
... We conclude this section with a few remarks on projections in Hilbert space .
Let E be a projection in Hilbert space H , and let E * be its Hilbert space adjoint .
Page 514
19 If E is a projection with n dimensional range , then E * is a projection with n
dimensional range . 20 A projection has finite dimensional range if and only if it is
compact . 21 A linear mapping E such that E2 = E is a projection ( i.e. , is
bounded ) ...
19 If E is a projection with n dimensional range , then E * is a projection with n
dimensional range . 20 A projection has finite dimensional range if and only if it is
compact . 21 A linear mapping E such that E2 = E is a projection ( i.e. , is
bounded ) ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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