Linear Operators, Part 2 |
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Results 1-3 of 56
Page 929
... invariant subspaces of X with respect to T , then M is said to reduce T. It is not difficult to see that a non - trivial subspace of Hilbert space may be an invariant subspace for an opera- tor but not reduce the operator . In fact , an ...
... invariant subspaces of X with respect to T , then M is said to reduce T. It is not difficult to see that a non - trivial subspace of Hilbert space may be an invariant subspace for an opera- tor but not reduce the operator . In fact , an ...
Page 930
... invariant subspaces for a given operator . It is not known whether every 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 ...
... invariant subspaces for a given operator . It is not known whether every 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 ...
Page 1911
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90-91 ) in a linear space , II.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Invariant subspace , definition of , X.9 ( 929 ) ...
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90-91 ) in a linear space , II.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Invariant subspace , definition of , X.9 ( 929 ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero