Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 877
... element y in Y has an inverse in X if and only if it has an inverse in Y. Consequently the spectrum of y as an element of Y is the same as its spectrum as an element of X. PROOF . If y1 exists as an element of then , since X and Y have ...
... element y in Y has an inverse in X if and only if it has an inverse in Y. Consequently the spectrum of y as an element of Y is the same as its spectrum as an element of X. PROOF . If y1 exists as an element of then , since X and Y have ...
Page 878
... elements determines the * -iso- morphism uniquely and we are thus led to the following definition . 12 DEFINITION . Let a be an element of a commutative B * -alge- bra and let fe C ( σ ( x ) ) . By f ( x ) will be meant the element in B ...
... elements determines the * -iso- morphism uniquely and we are thus led to the following definition . 12 DEFINITION . Let a be an element of a commutative B * -alge- bra and let fe C ( σ ( x ) ) . By f ( x ) will be meant the element in B ...
Page 1339
... elements is a { u ,, } - null element . Since a scalar multiple of a { u } -null element is evidently a { u } -null element , the family N ( { μ ;; } ) of { u } -null elements is a linear subspace of Lo ( { } ) . We shall follow the ...
... elements is a { u ,, } - null element . Since a scalar multiple of a { u } -null element is evidently a { u } -null element , the family N ( { μ ;; } ) of { u } -null elements is a linear subspace of Lo ( { } ) . We shall follow the ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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