Search results
Results From The WOW.Com Content Network
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.
Curl, (with operator symbol ) is a vector operator that measures a vector field's curling (winding around, rotating around) trend about a given point. As an extension of vector calculus operators to physics, engineering and tensor spaces, grad, div and curl operators also are often associated with tensor calculus as well as vector calculus.
Corollary — If a sequence of bounded operators () converges pointwise, that is, the limit of (()) exists for all , then these pointwise limits define a bounded linear operator . The above corollary does not claim that T n {\displaystyle T_{n}} converges to T {\displaystyle T} in operator norm, that is, uniformly on bounded sets.
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators , and consideration may be given to nonlinear operators .
Bounded operator, a linear transformation L between normed vector spaces for which the ratio of the norm of L(v) to that of v is bounded by the same number over all non-zero vectors v. Unbounded operator, a linear operator defined on a subspace; Bounded poset, a partially ordered set that has both a greatest and a least element
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 ...
What links here; Related changes; Upload file; Special pages; Permanent link; Page information; Cite this page; Get shortened URL; Download QR code
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 ...