## Linear Operators: Spectral theory |

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The inverse of a

only if its domain is

which maps ( x , y ] into [ y , x ] then I ( T - 1 ) = A T ( T ) which shows that T is

The inverse of a

**closed**operator is**closed**. A bounded operator is**closed**if andonly if its domain is

**closed**. Proof . If A , is the isometric automorphism in H oHwhich maps ( x , y ] into [ y , x ] then I ( T - 1 ) = A T ( T ) which shows that T is

**closed**...Page 1226

Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense

domain has a unique minimal

make the following definition . 7 DEFINITION . The minimal

Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense

domain has a unique minimal

**closed**symmetric extension . This fact leads us tomake the following definition . 7 DEFINITION . The minimal

**closed**symmetric ...Page 1393

We begin by defining a certain type of " spectrum ” for the formal differential

operator t . 1 DEFINITION . Let T be a

set of complex numbers 2 such that the range of AI -T is not

We begin by defining a certain type of " spectrum ” for the formal differential

operator t . 1 DEFINITION . Let T be a

**closed**operator in Hilbert space . Then theset of complex numbers 2 such that the range of AI -T is not

**closed**is called the ...### What people are saying - Write a review

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