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

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Page 1990

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. for some E - measurable and essentially bounded complex

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. for some E - measurable and essentially bounded complex

**valued**function â on RN . Before illustrating the results of the preceding section ...Page 1991

exists for every vector

measurable . In particular , if f is continuous and has its values in a compact set ,

it is l - measurable and thus integrable . For , in this case , the range of f may be

covered ...

exists for every vector

**valued**function f on RN which is bounded and d -measurable . In particular , if f is continuous and has its values in a compact set ,

it is l - measurable and thus integrable . For , in this case , the range of f may be

covered ...

Page 2092

The single

not have the single

S . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man [ 1 ] gave necessary conditions for

...

The single

**valued**extension property . The example of an operator which doesnot have the single

**valued**extension property that is given in Section 2 is due toS . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man [ 1 ] gave necessary conditions for

...

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero