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 |
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Page 2232
... ( Q ) and y = Qx . This shows that Q is closed . Let { n } be a second increasing sequence of elements of 2 such that E ( \ % = 1 ễn ) = I , and let Q be defined by the equations D ( Q ) = { x lim QoE ( ē , ) x exists } , Qx - o + น = lim ...
... ( Q ) and y = Qx . This shows that Q is closed . Let { n } be a second increasing sequence of elements of 2 such that E ( \ % = 1 ễn ) = I , and let Q be defined by the equations D ( Q ) = { x lim QoE ( ē , ) x exists } , Qx - o + น = lim ...
Page 2415
... q ( A1 ) ) - 1 = B exists , and is bounded and everywhere — 1 defined . If T1 is the closed restriction of T +9 ( A1 ) ... Let be a complex B - space . Let D be a subdomain of the complex plane which is not dense in the complex plane . Let ...
... q ( A1 ) ) - 1 = B exists , and is bounded and everywhere — 1 defined . If T1 is the closed restriction of T +9 ( A1 ) ... Let be a complex B - space . Let D be a subdomain of the complex plane which is not dense in the complex plane . Let ...
Page 2486
... q ( f , q ) . Let c be real . ( a ) Show that the equation W ( H + cT ) = HW has the formal solution WI + г . ( A ) , where A is the integral operator whose kernel A ( x , y ) is defined by = A ( x , y ) va ( x ) ( v , q ( y ) ) , v ɛ H ...
... q ( f , q ) . Let c be real . ( a ) Show that the equation W ( H + cT ) = HW has the formal solution WI + г . ( A ) , where A is the integral operator whose kernel A ( x , y ) is defined by = A ( x , y ) va ( x ) ( v , q ( y ) ) , v ɛ H ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero