Linear Operators, Part 2 |
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Page 929
... subspace which is neither { 0 } nor X for which we have TMCM , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If X is a Hilbert space and if both M and its ortho- complement XM are invariant subspaces of ...
... subspace which is neither { 0 } nor X for which we have TMCM , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If X is a Hilbert space and if both M and its ortho- complement XM are invariant subspaces of ...
Page 930
... 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 linear ...
... 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 linear ...
Page 1228
... subspace of D ( T * ) in- cluding D ( T ) , put S1n ( D , D_ ) . Clearly , 1 is closed and → + symmetric , and S 2 ... subspace of D + → D_ , and S = D ( T ) → S1 . ( a ) The space is symmetric if and only if 1 is the graph of an ...
... subspace of D ( T * ) in- cluding D ( T ) , put S1n ( D , D_ ) . Clearly , 1 is closed and → + symmetric , and S 2 ... subspace of D + → D_ , and S = D ( T ) → S1 . ( a ) The space is symmetric if and only if 1 is the graph of an ...
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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero