Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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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 ... In their proof , they proved Lemma 3.5 by using a fairly deep result of Šilov that was not generally available .
The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the results given in Section ... In their proof , they proved Lemma 3.5 by using a fairly deep result of Šilov that was not generally available .
Page 928
Mimura [ 1 ] simplified Riesz's proof , and extended the result to unbounded operators . A more elementary proof was given by Sz . - Nagy ( 3 ; pp . 63-65 ] ( see also Riesz and Sz . - Nagy [ 1 ; Sec .
Mimura [ 1 ] simplified Riesz's proof , and extended the result to unbounded operators . A more elementary proof was given by Sz . - Nagy ( 3 ; pp . 63-65 ] ( see also Riesz and Sz . - Nagy [ 1 ; Sec .
Page 1156
The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example Theorem 3.16 ... 2 ] = 2 " where ne R ( so that n is a positive or negative integer ) and i E Ř . We now state a result which ...
The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example Theorem 3.16 ... 2 ] = 2 " where ne R ( so that n is a positive or negative integer ) and i E Ř . We now state a result which ...
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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero