Linear Operators: Spectral operators |
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Page 868
This mapping a -> x(JR) of 3 into the field p of complex numbers is clearly a
homomorphism. Since la (JR) s r. this homomorphism is continuous. 2 LEMMA.
Let u be a non-zero homomorphism of the commutative B-algebra & onto the field
of ...
This mapping a -> x(JR) of 3 into the field p of complex numbers is clearly a
homomorphism. Since la (JR) s r. this homomorphism is continuous. 2 LEMMA.
Let u be a non-zero homomorphism of the commutative B-algebra & onto the field
of ...
Page 872
The number r(A) is clearly independent of the particular sequence {P,} used to
define it. For a fixed Zoe G the map a -- a (20) is a homomorphism of 3 into the
field of complex numbers. Thus by Lemma 2 there is a maximal ideal Joo with a (
Jo) ...
The number r(A) is clearly independent of the particular sequence {P,} used to
define it. For a fixed Zoe G the map a -- a (20) is a homomorphism of 3 into the
field of complex numbers. Thus by Lemma 2 there is a maximal ideal Joo with a (
Jo) ...
Page 1157
Then a complex number t of modulus 1 is outside a (d) if and only if there exists a
function g which is analytic in a neighborhood of t and is such that g(z) = f(z) for
all z in this meighborhood for which |z| # 1. Making use of this theorem and an ...
Then a complex number t of modulus 1 is outside a (d) if and only if there exists a
function g which is analytic in a neighborhood of t and is such that g(z) = f(z) for
all z in this meighborhood for which |z| # 1. Making use of this theorem and an ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
4 Exercises | 879 |
Copyright | |
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero