bounded linear transformation

bounded linear transformation

[¦bau̇n·dəd ¦lin·ē·ər tranz·fər′mā·shən]
(mathematics)
A linear transformation T for which there is some positive number A such that the norm of T (x) is equal to or less than A times the norm of x for each x.
References in periodicals archive ?
By an operator we mean a bounded linear transformation of X into itself.
If M is the range of a bounded linear transformation between Banach spaces X and Y, then the answer is yes.