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A linear operator : between two topological vector spaces (TVSs) is called a bounded linear operator or just bounded if whenever is bounded in then () is bounded in . A subset of a TVS is called bounded (or more precisely, von Neumann bounded ) if every neighborhood of the origin absorbs it.
BlooP and FlooP (Bounded loop and Free loop) are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book Gödel, Escher, Bach. [1] BlooP is a Turing-incomplete programming language whose main control flow structure is a bounded loop (i.e. recursion is not permitted [ citation needed ] ).
A Banach space is said to have bounded approximation property (BAP), if it has the -AP for some . A Banach space is said to have metric approximation property ( MAP ), if it is 1-AP. A Banach space is said to have compact approximation property ( CAP ), if in the definition of AP an operator of finite rank is replaced with a compact operator.
A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...
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, 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 ...
The Parsons problem format is used in the learning and teaching of computer programming. Dale Parsons and Patricia Haden of Otago Polytechnic developed Parsons's Programming Puzzles to aid the mastery of basic syntactic and logical constructs of computer programming languages, in particular Turbo Pascal, [1] although any programming language ...
Thus a unitary operator is a bounded linear operator that is both an isometry and a coisometry, [1] or, equivalently, a surjective isometry. [2] An equivalent definition is the following: Definition 2. A unitary operator is a bounded linear operator U : H → H on a Hilbert space H for which the following hold: U is surjective, and
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem [1] (named after Stefan Banach and Juliusz Schauder), is a fundamental result that states that if a bounded or continuous linear operator between Banach spaces is surjective then it is an open map.