Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 63
Page 1937
... matrix and a nilpotent operator N == 1 ( T — λ , I ) E ( λ ̧ ) . Stated in other terms , this classical reduction of Jordan asserts that every finite square matrix of complex numbers is equivalent to the sum of a diagonal matrix and a ...
... matrix and a nilpotent operator N == 1 ( T — λ , I ) E ( λ ̧ ) . Stated in other terms , this classical reduction of Jordan asserts that every finite square matrix of complex numbers is equivalent to the sum of a diagonal matrix and a ...
Page 2011
... matrices  ( s ) = ( âƒ1⁄2 ( 8 ) ) whose elements are measurable complex valued functions defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( s ) ...
... matrices  ( s ) = ( âƒ1⁄2 ( 8 ) ) whose elements are measurable complex valued functions defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( s ) ...
Page 2327
... matrix whose elements are given by the equation ( 5 ) , so that the elements M ( u ) -1M ( u ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then M1 ( μ ) depends analytically on μ , li , k≤n . Consider ...
... matrix whose elements are given by the equation ( 5 ) , so that the elements M ( u ) -1M ( u ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then M1 ( μ ) depends analytically on μ , li , k≤n . Consider ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
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