## Linear Operators: Spectral theory |

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Page 1036

Then the infinite product hi PA ( T ) 1 edia

analytic for a +0 . For each fixed 1 # 0 , P. ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . PROOF . First note

that if ...

Then the infinite product hi PA ( T ) 1 edia

**converges**and defines a functionanalytic for a +0 . For each fixed 1 # 0 , P. ( T ) is a continuous complex valued

function on the B - space of all Hilbert - Schmidt operators . PROOF . First note

that if ...

Page 1420

Indeed , let { { n } be a sequence in D ( Ti ( t ) ) . Suppose that { / }

zero in the topology of D ( T ( T ) ) . Then , by assumption ( b ) , { { n }

zero in the topology of D ( T2 ( t + r ' ) ) . Conversely , let { In }

...

Indeed , let { { n } be a sequence in D ( Ti ( t ) ) . Suppose that { / }

**converges**tozero in the topology of D ( T ( T ) ) . Then , by assumption ( b ) , { { n }

**converges**tozero in the topology of D ( T2 ( t + r ' ) ) . Conversely , let { In }

**converge**to zero in...

Page 1664

The Fourier series of an element F in D , ( C )

Proof . It follows from the Definition 37 of the topology in D ( C ) that it suffices to

show that ( 2π ) -η Σ F ,

The Fourier series of an element F in D , ( C )

**converges**unconditionally to F.Proof . It follows from the Definition 37 of the topology in D ( C ) that it suffices to

show that ( 2π ) -η Σ F ,

**converges**unconditionally to F ( q ) for each q in C ( C ) .### What people are saying - Write a review

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