New forms of bilateral inequalities for <i>K</i> - <i>g</i> -frames

Abstract In this work, several bilateral inequalities for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>K</m:mi> </m:math> K - <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>g</m:mi> </m:math> g -frames in subspaces are established, drawing support from two kinds of operators induced, respectively, by the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>K</m:mi> </m:math> K - <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>g</m:mi> </m:math> g -frame itself and the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>K</m:mi> </m:math> K -dual pair, which, compared with previous ones concerning this topic, possess novel structures. It is indicated that new types of inequalities for some other generalized frames can be naturally presented following our approaches.