Linear Operators: General theory |
From inside the book
Results 1-3 of 33
Page 4
... respectively . Finally if z is a complex number and z = x + -iy , where x and y are real , then x and y are called the real part and the imaginary part of z and are denoted by R ( z ) and I ( z ) , respectively . 2. Partially Ordered ...
... respectively . Finally if z is a complex number and z = x + -iy , where x and y are real , then x and y are called the real part and the imaginary part of z and are denoted by R ( z ) and I ( z ) , respectively . 2. Partially Ordered ...
Page 484
... respectively . The following result shows that , if T is weakly compact , its adjoint T * has a stronger continuity property . 7 LEMMA . An operator in B ( X , Y ) is weakly compact if and only if its adjoint is continuous with respect ...
... respectively . The following result shows that , if T is weakly compact , its adjoint T * has a stronger continuity property . 7 LEMMA . An operator in B ( X , Y ) is weakly compact if and only if its adjoint is continuous with respect ...
Page 485
... respectively . If S , S ** are the closed unit spheres in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by Theorem V.4.5 , xS is X * -dense in S ** , and so , from the continuity of T ** we see that T ...
... respectively . If S , S ** are the closed unit spheres in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by Theorem V.4.5 , xS is X * -dense in S ** , and so , from the continuity of T ** we see that T ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ