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

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Page 1909

The exclusion of the theory of spectral operators from Part II was not due solely to

the growth of the literature in this field , but was determined also by our desire to

The exclusion of the theory of spectral operators from Part II was not due solely to

the growth of the literature in this field , but was determined also by our desire to

**present**a number of important applications of the general theory of spectral ...Page 2058

In explaining these implications in nonmathematical terms he envisaged , in his

Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator

who could , upon having complete knowledge of the

...

In explaining these implications in nonmathematical terms he envisaged , in his

Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator

who could , upon having complete knowledge of the

**present**state of the universe...

Page 2227

The

spectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

The

**present**chapter is an attempt to make the corresponding step in the theory ofspectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

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### Common terms and phrases

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