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Page 860
A B - algebra X is commutative in case xy = yx for all x and y in X. X An involution in a B - algebra X is a mapping ... the exception of L ( -00,00 ) and the class of analytic functions , are commutative B - algebras with involutions .
A B - algebra X is commutative in case xy = yx for all x and y in X. X An involution in a B - algebra X is a mapping ... the exception of L ( -00,00 ) and the class of analytic functions , are commutative B - algebras with involutions .
Page 875
The algebra B ( H ) of all bounded linear operators in Hilbert space H in which the operation * of involution is defined by equation ( i ) is a B ... Our chief objective in this section is to characterize commutative B * -algebras .
The algebra B ( H ) of all bounded linear operators in Hilbert space H in which the operation * of involution is defined by equation ( i ) is a B ... Our chief objective in this section is to characterize commutative B * -algebras .
Page 979
besque be based upon two closely related commutative algebras of operators in the Hilbert space L2 ( R ) . One of these algebras , namely the algebra A of the preceding section , we have met before . For convenience , its definition and ...
besque be based upon two closely related commutative algebras of operators in the Hilbert space L2 ( R ) . One of these algebras , namely the algebra A of the preceding section , we have met before . For convenience , its definition and ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
Copyright | |
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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero