Continuous Framings with Invariant Subspace Problem and Order Asymptotically Isometric Copies in Banach Function Spaces

Abstract

Frames and continuous framings for Banach spaces are constructed . We introduce the Frames associated and expansions with measurable spaces, in separable Banach spaces , Riesz bases, and sampling expansions in Banach spaces by semi-inner products . A solution to the invariant subspace problem on the Lebesgue space was given ,also the invariant subspace problem for non-Archimedean Fre ̀chet spaces , Banach spaces , classical spaces of functions and Köthe spaces are obtained . The Daugavet property in the space of Musielak-Orlicz was studied and the order asymptotically isometric and isometric copies of〖 L〗^1,L^∞, l^1 〖,l〗^∞ and c_0 in Orlicz and Banach function spaces are characterized .