Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 929
... subspace which is neither { 0 } nor X for which we have TM M CM , 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 ...
... subspace which is neither { 0 } nor X for which we have TM M CM , 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 ...
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 S1 = Sn ( D. → D_ ) . Clearly , 1 is closed and symmetric , and S 2 ... subspace of DD , and S = D ( T ) → S1 . ( a ) The space is symmetric if and only if 1 is the graph of an isometric ...
... subspace of D ( T * ) in- cluding D ( T ) , put S1 = Sn ( D. → D_ ) . Clearly , 1 is closed and symmetric , and S 2 ... subspace of DD , and S = D ( T ) → S1 . ( a ) The space is symmetric if and only if 1 is the graph of an isometric ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero