continuous operator

(redirected from Bounded operator)
Also found in: Wikipedia.

continuous operator

[kən¦tin·yə·wəs ′äp·ə‚rād·ər]
(mathematics)
A linear transformation of Banach spaces which is continuous with respect to their topologies.
References in periodicals archive ?
0] induces a bounded operator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on [L.
ran(C)] is a bounded operator from ran(C) onto ran(C) with bounded inverse.
k]}, for any bounded operator W : H [right arrow] H.
Notice that, in the case that A is a bounded operator, the left-definite theory is trivial but, when A is unbounded, the theory has substance.
Moreover, a look at the proof of Observation 2 reveals that every translation invariant, linear, and bounded operator T : W [right arrow] [L.
m] is a bounded operator and the following inequality holds:
0] induces a bounded operator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for every f [member of] [L.
1]) is a bounded operator (and gives a norm estimate depending on the unknown constant K').
Clearly for two Bessel sequences it is well-defined as linear bounded operator because