Linear Operators: Spectral operators |
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Page 2312
... Banach theorem ( II.3.13 ) there exists a y * in Y * such that y * ( y ) # 0 , y * Tz 0 for z in D ( T ) . Then it ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
... Banach theorem ( II.3.13 ) there exists a y * in Y * such that y * ( y ) # 0 , y * Tz 0 for z in D ( T ) . Then it ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
Page 2563
... Banach space . Proc . London Math . Soc . ( 3 ) 3 , 368–377 ( 1953 ) . 6. Operators with a Fredholm theory . J. London Math . Soc . 29 , 318-326 ( 1954 ) . Rutman , M. A. ( see Krein , M. G. ) Saffern , W. W. 1. Subscalar operators ...
... Banach space . Proc . London Math . Soc . ( 3 ) 3 , 368–377 ( 1953 ) . 6. Operators with a Fredholm theory . J. London Math . Soc . 29 , 318-326 ( 1954 ) . Rutman , M. A. ( see Krein , M. G. ) Saffern , W. W. 1. Subscalar operators ...
Page 2567
... Banach spaces . Colloq . Math . 8 , 141-198 ( 1961 ) . Determinants in Banach spaces . Studia Math . ( Ser . Specjalna ) Zeszyt . 1 , 111-116 ( 1963 ) . Silberstein , J. P. O. 2. Symmetrisable operators , I - III . I. J. Austral . Math ...
... Banach spaces . Colloq . Math . 8 , 141-198 ( 1961 ) . Determinants in Banach spaces . Studia Math . ( Ser . Specjalna ) Zeszyt . 1 , 111-116 ( 1963 ) . Silberstein , J. P. O. 2. Symmetrisable operators , I - III . I. J. Austral . Math ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero