transpose operator

Let X,Y be normed vector spacesPlanetmathPlanetmath and X,Y be their continuous dual spaces.

- Let T:XY be a bounded linear operator. The operator T:YX given by


is called the transpose operator of T or the conjugate operator of T.

It is clear that T is well defined, i.e. ϕTX, since the composition of two continuous linear operators is again a continuous linear operator.

Moreover, it can be easily checked that T is a bounded linear operator.

Remarks -

Title transpose operator
Canonical name TransposeOperator
Date of creation 2013-03-22 17:34:19
Last modified on 2013-03-22 17:34:19
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 5
Author asteroid (17536)
Entry type Definition
Classification msc 47A05
Classification msc 46-00
Synonym conjugate operator
Related topic Transpose
Related topic Adjoint5