## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1951

5 the compact operators form a closed twosided ideal in B ( X ) and so the

present corollary is immediate . Q . E . D . 4 COROLLARY . If T is

, then so are S , N , and every projection E ( o ) with 0 € 7 . PROOF . By Corollary

VI .

5 the compact operators form a closed twosided ideal in B ( X ) and so the

present corollary is immediate . Q . E . D . 4 COROLLARY . If T is

**weakly compact**, then so are S , N , and every projection E ( o ) with 0 € 7 . PROOF . By Corollary

VI .

Page 2110

In Walsh [ 3 ] this was extended to the case where E has the property that

such spaces are limits in the strong operator topology of finite dimensional ...

In Walsh [ 3 ] this was extended to the case where E has the property that

**weakly****compact**subsets are compact ( for example , l1 ) . Thus the scalar operators insuch spaces are limits in the strong operator topology of finite dimensional ...

Page 2186

Let A be an algebra of operators in the

which is the image under a continuous homomorphism S of the algebra C ( 1 ) of

all complex continuous functions on a

Let A be an algebra of operators in the

**weakly**complete complex B - space Xwhich is the image under a continuous homomorphism S of the algebra C ( 1 ) of

all complex continuous functions on a

**compact**space 1 . Then there exists a ...### What people are saying - Write a review

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