Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 891
Nelson Dunford, Jacob T. Schwartz. scalar function f with respect to the operator valued set function E. In the present chapter we shall only integrate bounded functions f and so the following discussion of the integral will be ...
Nelson Dunford, Jacob T. Schwartz. scalar function f with respect to the operator valued set function E. In the present chapter we shall only integrate bounded functions f and so the following discussion of the integral will be ...
Page 1178
... functions boundedly into the space L ( l1⁄2 ) of vector- valued functions . Let M be the mapping in L , ( l ) which maps the vector - valued function whose nth component has the Fourier transform ( 5 ) into the vector - valued function ...
... functions boundedly into the space L ( l1⁄2 ) of vector- valued functions . Let M be the mapping in L , ( l ) which maps the vector - valued function whose nth component has the Fourier transform ( 5 ) into the vector - valued function ...
Page 1922
... function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix , definition , VI.9.28 ( 515 ) of two ...
... function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix , definition , VI.9.28 ( 515 ) of two ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero