## Linear Operators: Spectral theory |

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Page 1188

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has

been

necessarily bounded and this concept is formulated in the following

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has

been

**defined**by the identity ( Tx , y ) ... space adjoint of an operator which is notnecessarily bounded and this concept is formulated in the following

**definition**.Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

self adjoint operator T and let f be a complex Borel function

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

**defines**an ... Let E be the resolution of the identity for theself adjoint operator T and let f be a complex Borel function

**defined**E - almost ...Page 1548

extensions of S and Ŝ respectively , and let 2n ( T ) and an ( Î ) be the numbers

22n ( † ) , n 2 1 . D11 Let T , be a self adjoint operator in Hilbert space Hi , and let

...

extensions of S and Ŝ respectively , and let 2n ( T ) and an ( Î ) be the numbers

**defined**for the self adjoint operators T and Î as in Exercise D2 . Show that an ( T )22n ( † ) , n 2 1 . D11 Let T , be a self adjoint operator in Hilbert space Hi , and let

...

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