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 1273
... linear operator with dense domain , let y ( T ) be the set of all complex numbers & such that the inverse operator ( T — ¿ I ) −1 exists and is bounded on its domain . The set y ( T ) is called the domain of regularity of T ( or the ...
... linear operator with dense domain , let y ( T ) be the set of all complex numbers & such that the inverse operator ( T — ¿ I ) −1 exists and is bounded on its domain . The set y ( T ) is called the domain of regularity of T ( or the ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero