## Linear Operators: Spectral operators |

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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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algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete consider constant contained 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero