Some linear maps preserving continuous frames for operators in Hilbert spaces

Abstract

In this paper two methods for generating continuous K -frames for a Hilbert spaceH are introduced, where K is a bounded operator on H. Both methods transform acontinuous K -frame of H into another continuous K -frame of H. The first one hasan algebraic approach: a continuous K -frame for HAis shown to be preserved bysome operators with specific algebraic properties, where HAdenotes a module whosemodule operation depends on another fixed bounded operator A on H. The othermethod preserves a continuous K -frame using some minimal projections defined bymeans of the Moore-Penrose inverse of a closed range operator. Also, some examplesillustrate the results.