Linear Operators: General theory |
From inside the book
Results 1-3 of 75
Page 611
... operators which are not compact but whose spectra are the same as that of a compact operator . This is not true for normal operators in Hilbert space ( see Sz . - Nagy [ 3 ; p . 55 ] ) . Similarly von Neumann [ 6 ; p . 16 ] has shown ...
... operators which are not compact but whose spectra are the same as that of a compact operator . This is not true for normal operators in Hilbert space ( see Sz . - Nagy [ 3 ; p . 55 ] ) . Similarly von Neumann [ 6 ; p . 16 ] has shown ...
Page 745
... operators . Proc . Nat . Acad . Sci . 38 , 732-737 ( 1952 ) . 2 . 3 . The spectral representation of ordinary self - adjoint differential operators ... Hilbert space . Proc . London Math . Soc . ( 2 ) 50 , 3 . 11-55 ( 1948 ) . One - parameter ...
... operators . Proc . Nat . Acad . Sci . 38 , 732-737 ( 1952 ) . 2 . 3 . The spectral representation of ordinary self - adjoint differential operators ... Hilbert space . Proc . London Math . Soc . ( 2 ) 50 , 3 . 11-55 ( 1948 ) . One - parameter ...
Page 809
... operators in Hilbert space . Proc . Cambridge Philos . Soc . 49 , 201-212 ( 1953 ) . Šilov , G. ( see also Gelfand , I. ) 1 . 2 . 3 . 4 . 5 . Ideals and subrings of the ring of continuous functions . Doklady Akad . Nauk SSSR ( N. S. ) ...
... operators in Hilbert space . Proc . Cambridge Philos . Soc . 49 , 201-212 ( 1953 ) . Šilov , G. ( see also Gelfand , I. ) 1 . 2 . 3 . 4 . 5 . Ideals and subrings of the ring of continuous functions . Doklady Akad . Nauk SSSR ( N. S. ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ