Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1100
... prove ( b ) in general , we have only to prove ( b ) in the special case in which A and B have finite - dimensional ranges . But then the inequality in ( b ) is plainly a special case of ( a ) , while the identity ( 3 ) follows readily ...
... prove ( b ) in general , we have only to prove ( b ) in the special case in which A and B have finite - dimensional ranges . But then the inequality in ( b ) is plainly a special case of ( a ) , while the identity ( 3 ) follows readily ...
Page 1393
... prove that TX is closed if TY is closed , we shall prove more generally that the sum of a closed subspace 3 of a B - space , and of a finite dimensional space îì , is closed . It is clear that proceed- ing inductively we may assume ...
... prove that TX is closed if TY is closed , we shall prove more generally that the sum of a closed subspace 3 of a B - space , and of a finite dimensional space îì , is closed . It is clear that proceed- ing inductively we may assume ...
Page 1563
... Prove that | ( 2 − t ) fn | = O ( √ ( bn — ɑn ) ) . ( b ) Prove that the essential spectrum of t contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the ...
... Prove that | ( 2 − t ) fn | = O ( √ ( bn — ɑn ) ) . ( b ) Prove that the essential spectrum of t contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose that the function q is bounded below . Suppose that the ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 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