Linear Operators: General theory |
From inside the book
Results 1-3 of 64
Page 37
... linear transformation which maps into 3. If T is a linear operator on X to X , it is said to be a linear operator in X. For such operators the symbol T2 is used for TT , and , inductively , Tn for T - 1T . The symbol I is used for the ...
... linear transformation which maps into 3. If T is a linear operator on X to X , it is said to be a linear operator in X. For such operators the symbol T2 is used for TT , and , inductively , Tn for T - 1T . The symbol I is used for the ...
Page 494
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) , and ...
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) , and ...
Page 605
... operator ( Tx ) ( t ) = x ' ( t ) with domain D ( T ) = { x | x is absolutely continuous on each finite interval , x ' e L „ ( - ∞ , ∞ ) } . Show that ( a ) T is a closed unbounded linear operator whose domain is dense for p ...
... operator ( Tx ) ( t ) = x ' ( t ) with domain D ( T ) = { x | x is absolutely continuous on each finite interval , x ' e L „ ( - ∞ , ∞ ) } . Show that ( a ) T is a closed unbounded linear operator whose domain is dense for p ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ