# eBook CBMS Unitary Dilations of Hilbert Space Operators and Related Topics download

## by B. Sz.-Nagy

**ISBN:**0821816691

**Author:**B. Sz.-Nagy

**Publisher:**American Mathematical Society (December 31, 1974)

**Language:**English

**Pages:**54

**ePub:**1770 kb

**Fb2:**1926 kb

**Rating:**4.6

**Other formats:**mbr rtf mbr rtf

**Category:**Math Sciences

**Subcategory:**Mathematics

A co-publication of the AMS and CBMS.

A co-publication of the AMS and CBMS. A good introduction for the reader before taking on the book by C. Foiaş and the author Harmonic Analysis of Operators on Hilbert Space, North- Holland, 1970]. Go . current document Publication list for all documents.

Go to book description Print multiple pages. 4 BEL A S. NAGY the symmetr y propert y o f th e inne r product-i n cas e n m also

Go to book description Print multiple pages. You have printed 0 times in the last 24 hours. Your print count will reset on at. You may print 0 more time(s) before then. NAGY the symmetr y propert y o f th e inne r product-i n cas e n m also. Henc e w e conclud e that th e ma p OO OO £ V' nhn M £ U" nhn (h n e § ; h n Q fo r n larg e enough ) - oo -oo is isometric, an d therefor e extend s b y continuit y t o a n isometr y cf o f ft' ont o ft". This isometr y leave s th e vector s i n § invariant, an d carrie s U' int o (/", . cfU' U f. Thu s i f w e disregar d suc h isometri c isomorphism s cf y th e minima l unitar y dila - tion o f T is unique.

unitary di~ lation U on a Hilbert space ft. One can require that this unitary dilation be minimal in the sense (. 3) V U n§ ft; U is then determined by T uniquely {that is, up to an isometric isomorphism leaving the vectors of § invariant). For m th e Hilber t spac e ft oi vector s (. -, h v h v g j, h v b v - ^ with component s h Q e §, h n e 2), h e 3 fo r 1, an d nor m 1/2 IWI Z H OO, and embe d § i n ft b y identifyin g h e. S p wit h y,,, 0, ]T], 0,,, y - Th e orthogona l projection P ^ i s the n give n b y P ^ ..

Goodreads helps you keep track of books you want to read. See a Problem? We’d love your help. Start by marking Unitary Dilations of Hilbert Space Operators and Related Topics, as Want to Read: Want to Read savin. ant to Read. Read by Bela Szzokefalvi-Nagy.

operators related to compact operators by Carl Pearcy and Allen L. Shields. Unitary dilations of Hilbert space operators and related topics by B. S. Nagy, CBMS No. 19. Amer. Two results concerning operators on finite dimensional complex vector. spaces lead one to feel that one has a fairly good grasp of their structure.

Part of the Operator Theory: Advances and Applications book series (OT .

Part of the Operator Theory: Advances and Applications book series (OT, volume 127). A characterization for a commutative family of operators to have a unitary power dilation is given here. The problem is converted into one on extension of positive definite operator valued functions defined on a subset of a -semigroup. As a byproduct, a solution to Krein’s extension problem for positive definite functions on subsets of ℝ N. Keywords. B. Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, Akadémiai Kiadö and North-Holland, Budapest and Amsterdam - London, 1970. zbMATHGoogle Scholar.

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In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the orthogonal projection onto H is T. More formally. More formally, let T be a bounded operator on some Hilbert space H, and H be a subspace of a larger Hilbert space H'. A bounded operator V on H' is a dilation of T if. where

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. Since then, this work has influenced many. Harmonic Analysis of Operators on Hilbert Space. Explores harmonic analysis techniques for the study of the mathematical concept of Hilbert space. Focusing mainly on operator theories and developments, the text discusses two specific operator classes.