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 σ ( 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 σ ( 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 ( t ) ) which is a compact operator from D ( T1 ( T ) ) to La ( 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 ( t ) ) which is a compact operator from D ( T1 ( T ) ) to La ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of T1 ( T ) + B . B. Non - Self Adjoint ...
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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero