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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.
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Praktičan vodič kroz Beograd sa pevanjem i plakanjem Practical Guide to Belgrade with Singing and Crying: Bojan Vuletić: Marko Janketić Julie Gayet Anita Mančić Jean-Marc Barr: Comedy / Drama / Romance: The Scent of Rain in the Balkans [1] Miris kiše na Balkanu: Ljubiša Samardžić: Mirka Vasiljević: Drama, Romance: 2012: Klip Clip ...
In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus, but it was also proven independently by Hans Hahn.
Since the graph of T is closed, the proof reduces to the case when : is a bounded operator between Banach spaces. Now, T {\displaystyle T} factors as X → p X / ker T → T 0 im T ↪ i Y {\displaystyle X{\overset {p}{\to }}X/\operatorname {ker} T{\overset {T_{0}}{\to }}\operatorname {im} T{\overset {i}{\hookrightarrow }}Y} .
A T ∈ L(H) is a Fredholm operator if and only if T is invertible modulo compact perturbation, i.e. TS = I + C 1 and ST = I + C 2 for some bounded operator S and compact operators C 1 and C 2. In other words, an operator T ∈ L(H) is Fredholm, in the classical sense, if and only if its projection in the Calkin algebra is invertible.
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 ...
Film Director Writer Producer Awards / Notes 1980 Ko to tamo peva: Yes No No Bronze Arena at Pula Film Festival: 1982 Maratonci trče počasni krug: Yes No No Jury prize at Montréal World Film Festival: 1983 Kako sam sistematski uništen od idiota: Yes Yes No 1984 Davitelj protiv davitelja: Yes Yes No 1988 Tajna manastirske rakije: Yes No No 2003