## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

### From inside the book

Results 1-3 of 79

Page 884

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the

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

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

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 ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

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