Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 76
Page 2108
... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : X - C such that a Sf ( x ) μ ( dx ) . It follows that there exists a spectral measure va defined on a compact subset of C to A such ...
... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : X - C such that a Sf ( x ) μ ( dx ) . It follows that there exists a spectral measure va defined on a compact subset of C to A such ...
Page 2405
... exists for μ - almost all s , and that , writing If , for the norm of an element f of L , ( S , 2 , μ ) , we have | Ãh | , ≤ { A } , [ h ] , . Thus , using Theorem III.2.22 ( a ) , we see that if 2 ≤r < ∞ , and if g is any complex ...
... exists for μ - almost all s , and that , writing If , for the norm of an element f of L , ( S , 2 , μ ) , we have | Ãh | , ≤ { A } , [ h ] , . Thus , using Theorem III.2.22 ( a ) , we see that if 2 ≤r < ∞ , and if g is any complex ...
Page 2418
... exists almost everywhere for each ƒ¤Î „ ( D , Y ) , and , using Lemma 5 once more , the integral ( 74 ) A2 ( z , z ′ ) \ f ↓ 2 | 43 ( 2 " , 2 ) } { | | 42 ( 2 , 2 ) | | ( = ' ) de ' dy dx dy Sol | A1 ( z ′′ , D D exists for almost all ...
... exists almost everywhere for each ƒ¤Î „ ( D , Y ) , and , using Lemma 5 once more , the integral ( 74 ) A2 ( z , z ′ ) \ f ↓ 2 | 43 ( 2 " , 2 ) } { | | 42 ( 2 , 2 ) | | ( = ' ) de ' dy dx dy Sol | A1 ( z ′′ , D D exists for almost all ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero