Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1257
... isometric transformation ( which is not necessarily everywhere defined ) . Show the following : The operator T is ... isometric operator such that I - V is one - to - one and has a dense range , equation [ †† ] defines a symmetric ...
... isometric transformation ( which is not necessarily everywhere defined ) . Show the following : The operator T is ... isometric operator such that I - V is one - to - one and has a dense range , equation [ †† ] defines a symmetric ...
Page 1258
... isometric operator V. ) 7 If { T ( t ) } tzo is a strongly continuous semi - group of operators in Hilbert space ... isometric operators whose initial domains are is of the form iT , where T is a maximal symmetric operator with positive ...
... isometric operator V. ) 7 If { T ( t ) } tzo is a strongly continuous semi - group of operators in Hilbert space ... isometric operators whose initial domains are is of the form iT , where T is a maximal symmetric operator with positive ...
Page 1373
... isometric isomorphisms onto all of L2 ( ^ , { î ;; } ) and L2 ( 4 , { μ¿ ; } ) , respectively . Since d A [ [ " * 1 ... isometric isomorphism Ŷ of E ( A ) L2 ( I ) onto L¿ ( A , { ^ ;; } ) . It follows similarly that this same limit ...
... isometric isomorphisms onto all of L2 ( ^ , { î ;; } ) and L2 ( 4 , { μ¿ ; } ) , respectively . Since d A [ [ " * 1 ... isometric isomorphism Ŷ of E ( A ) L2 ( I ) onto L¿ ( A , { ^ ;; } ) . It follows similarly that this same limit ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero