## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 1010

The number || T || is sometimes called the Hilbert - Schmidt

. In this definition of the class HS a particular orthonormal sequence was used .

The number || T || is sometimes called the Hilbert - Schmidt

**norm**or the double -**norm**of T. The class of all Hilbert - Schmidt operators on H will be denoted by HS. In this definition of the class HS a particular orthonormal sequence was used .

Page 1015

If lim Tn T in the

integral in [ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII.6.3 it

is seen that , in the

If lim Tn T in the

**norm**of HS it follows from Lemma VII.6.5 that the contour C of theintegral in [ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII.6.3 it

is seen that , in the

**norm**of HS + , lim ( 2 , -T . ) - 1 = ( 1 , -T ] -1 uniformly for 2 in ...Page 1297

The first

Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( ) ) is

complete in the

as an ...

The first

**norm**is the**norm**of the pair [ f , T / ] as an element of the graph of Ti ( t ) .Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( ) ) is

complete in the

**norm**\ / lı . Since the two additional terms in 1/2 are the**norm**of fas an ...

### 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 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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero