If M is a finite complemented modular lattice with n atoms and D is a bounded distributive lattice, then the Priestley power M [D] is shown to be isomorphic to the poset of normal elements of Dn, thus solving a problem of E. T. Schmidt from 1974. It is shown that there exist a finite modular lattice A not having M4 as a sublattice and a finite modular lattice B such that A⊗B is not semimodular,...

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.