Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 15
Page 873
... compact Hausdorff space then it is homeomorphic with the structure space of C ( A ) . 18 COROLLARY . If A , and A2 are compact Hausdorff spaces such that the algebras С ( Â1 ) and C ( IX.2.17 873 COMMUTATIVE B - ALGEBRAS.
... compact Hausdorff space then it is homeomorphic with the structure space of C ( A ) . 18 COROLLARY . If A , and A2 are compact Hausdorff spaces such that the algebras С ( Â1 ) and C ( IX.2.17 873 COMMUTATIVE B - ALGEBRAS.
Page 880
... compact Hausdorff space , and let n ( S ) be the least number of generators of the algebra C ( S ) . Find n ( S ) for ( a ) The unit circle = 1 . ( b ) The unit sphere in three - dimensional Euclidean space . ( c ) The Hilbert cube { x ...
... compact Hausdorff space , and let n ( S ) be the least number of generators of the algebra C ( S ) . Find n ( S ) for ( a ) The unit circle = 1 . ( b ) The unit sphere in three - dimensional Euclidean space . ( c ) The Hilbert cube { x ...
Page 1150
... compact Abelian group . As remarked in the text , the development presented ... space , a fact that was occasionally used in the text . Next we shall state ... Hausdorff space and hence ( I.5.9 ) normal , and the set F , FU { 0 } is ...
... compact Abelian group . As remarked in the text , the development presented ... space , a fact that was occasionally used in the text . Next we shall state ... Hausdorff space and hence ( I.5.9 ) normal , and the set F , FU { 0 } is ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero