Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 71
Page 955
... denote the B * -algebra of operators A → { al } , where I is the identity operator in the Hilbert space L2 ( R ) , and where Д is the closure of A in the uniform operator topology . The letter M will denote the space of maximal ideals ...
... denote the B * -algebra of operators A → { al } , where I is the identity operator in the Hilbert space L2 ( R ) , and where Д is the closure of A in the uniform operator topology . The letter M will denote the space of maximal ideals ...
Page 1126
... denote by the letter U 。. Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU 。. Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident that ...
... denote by the letter U 。. Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU 。. Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident that ...
Page 1673
... denote the function in Co ( 11 ) defined by the equation y ( x ) = q ( M ( x ) ) ; ( ii ) for each F in D , ( I1 ) the symbol Fo M - 1 will denote the distribution G in D , ( 12 ) defined by the equation G ( p ) = F ( po M ) for 9 in Co ...
... denote the function in Co ( 11 ) defined by the equation y ( x ) = q ( M ( x ) ) ; ( ii ) for each F in D , ( I1 ) the symbol Fo M - 1 will denote the distribution G in D , ( 12 ) defined by the equation G ( p ) = F ( po M ) for 9 in Co ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero