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

### From inside the book

Results 1-3 of 72

Page 888

Here we have used the notations A i B and A v B for the intersection and union of two commuting

Here we have used the notations A i B and A v B for the intersection and union of two commuting

**projections**A and B. We ... Also the ranges of the intersection and union of two commuting**projection**operators are given by the equations ...Page 1123

We say that E is a subdiagonalizing

We say that E is a subdiagonalizing

**projection**for T if T leaves the range of E invariant , i.e. , if ETE = TE . ... Any operator T in Hilbert space admits a maximal totally ordered set F of orthogonal subdiagonalizing**projections**...Page 1126

Since each

Since each

**projection**in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of the**projections**Ej , it follows from ( 1 ) that the closure in $ ( xm ) of the vectors ( 4 ) is ...### 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