Linear Operators, Part 2 |
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Page 884
The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the results given in Section 1 are due . B- and B * -algebras . The results of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 ...
The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the results given in Section 1 are due . B- and B * -algebras . The results of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 ...
Page 909
The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for every x in H. Hence the characterization of In , Mn given in Theorem 3 shows that an Ellion for all n = 1 , 2 , .... - 5. Spectral Representation Let M ...
The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for every x in H. Hence the characterization of In , Mn given in Theorem 3 shows that an Ellion for all n = 1 , 2 , .... - 5. Spectral Representation Let M ...
Page 1273
The simplification , given by Freudenthal [ 3 ] , of Friedrichs ' proof is the one presented in the text . For another proof of the theorem , see Calkin 3 ] and Eberlein ( 2 ; p . 699 ) , and for applications to partial differential ...
The simplification , given by Freudenthal [ 3 ] , of Friedrichs ' proof is the one presented in the text . For another proof of the theorem , see Calkin 3 ] and Eberlein ( 2 ; p . 699 ) , and for applications to partial differential ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
13 other sections not shown
Common terms and phrases
additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators, Part 2 Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1982 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471869139, 9780471869139 |
| Export Citation | BiBTeX EndNote RefMan |