Linear Operators: Spectral theory |
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Page 930
... operator , distinct from the zero and identity operators , has a non - trivial invariant subspace . It is readily seen from Theorem VII.3.10 that if T is a bounded linear operator in a B - space X and if o ( T ) contains at least two ...
... operator , distinct from the zero and identity operators , has a non - trivial invariant subspace . It is readily seen from Theorem VII.3.10 that if T is a bounded linear operator in a B - space X and if o ( T ) contains at least two ...
Page 1016
... linear operator in Hilbert space are irrevocably lost , will be retained by Hilbert - Schmidt operators . To show that this is indeed the case we need to derive a variety of inequalities for operators in finite dimensional Hilbert ...
... linear operator in Hilbert space are irrevocably lost , will be retained by Hilbert - Schmidt operators . To show that this is indeed the case we need to derive a variety of inequalities for operators in finite dimensional Hilbert ...
Page 1540
... linear operator in L2 ( I ) defined in D ( T1 ( 7 ) ) which is a compact operator from D ( T1 ( 7 ) ) to L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of T1 ( t ) + B . B. Non - Self Adjoint ...
... linear operator in L2 ( I ) defined in D ( T1 ( 7 ) ) which is a compact operator from D ( T1 ( 7 ) ) to L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of T1 ( t ) + B . B. Non - Self Adjoint ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero