Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1180
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L ( ) , § denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L ( ) , § denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
Page 1262
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space H12H , and an orthogonal projection Qin , such that Ax = PQx , x = $ , P denoting the orthogonal projection of H1 on H. 29 Let { T } be a sequence of bounded ...
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space H12H , and an orthogonal projection Qin , such that Ax = PQx , x = $ , P denoting the orthogonal projection of H1 on H. 29 Let { T } be a sequence of bounded ...
Page 1773
Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex numbers , together with a complex function ( • , • ) defined on H × H with the following ... spaces , Hilbert space 1773 APPENDIX.
Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex numbers , together with a complex function ( • , • ) defined on H × H with the following ... spaces , Hilbert space 1773 APPENDIX.
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero