Operator theory

Contraction (operator theory)

In operator theory, a bounded operator T: X → Y between normed vector spaces X and Y is said to be a contraction if its operator norm ||T || ≤ 1. This notion is a special case of the concept of a contraction mapping, but every bounded operator becomes a contraction after suitable scaling. The analysis of contractions provides insight into the structure of operators, or a family of operators. The theory of contractions on Hilbert space is largely due to Béla Szőkefalvi-Nagy and Ciprian Foias. (Wikipedia).

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Related pages

Béla Szőkefalvi-Nagy | Operator norm | Normed vector space | Spectral theorem | Reducing subspace | Minimal polynomial (linear algebra) | Positive harmonic function | Ciprian Foias | Bounded operator | Unitary operator | Bochner's theorem | Square root of a matrix | Unbounded operator | Dilation (operator theory) | Isometry | Singular measure | Sz.-Nagy's dilation theorem | Blaschke product | Operator theory | Hilbert space | Contraction mapping | Hardy space