Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1026
... fact that tr ( T , T * ) = || T || 2 follow immediately from Definitions 1 and 17. Q.E.D. It follows readily from the results stated above that HS forms a Hilbert space under the inner product [ S , T ] = tr ( S , T * ) . Although this fact ...
... fact that tr ( T , T * ) = || T || 2 follow immediately from Definitions 1 and 17. Q.E.D. It follows readily from the results stated above that HS forms a Hilbert space under the inner product [ S , T ] = tr ( S , T * ) . Although this fact ...
Page 1245
... fact that each complex number a has a unique representation a where r≥ 0 , and | ei | 1. By analogy with the fact that r = we shall first seek to obtain the self adjoint operator A from the operator T * T . - α = reio , ( ãα ) , 1 ...
... fact that each complex number a has a unique representation a where r≥ 0 , and | ei | 1. By analogy with the fact that r = we shall first seek to obtain the self adjoint operator A from the operator T * T . - α = reio , ( ãα ) , 1 ...
Page 1348
... fact entire in 2. In the range suitable basis for the solutions of to λ < 0 , ¿ is imaginary , and an analytic expression like cos it is hard to work with because of the apparent ambiguity in the definition of 2. An analysis of the ...
... fact entire in 2. In the range suitable basis for the solutions of to λ < 0 , ¿ is imaginary , and an analytic expression like cos it is hard to work with because of the apparent ambiguity in the definition of 2. An analysis of 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