The set of tripotents in a JBW*-triple 21 with its natural ordering and with a largest element adjoined is shown to be a complete lattice, order isomorphic to the lattice of norm closed faces in the unit ball &"! of the predual 21* of 21 and anti-order isomorphic to the lattice of weak* closed faces of the unit ball Ulj in SI. As a consequence, the set of partial isometries in a W*-algebra with its natural ordering and again with a largest element adjoined forms a complete lattice and every non-empty weak* closed face of its unit ball is of the form M + (1 -MM*) 21(1 -« * « ) ! for some unique partial isometry M.
The set %(C)~ consisting of the partially ordered set °U(G) of tripotents in a JBW*-triple C with a greatest element adjoined forms a complete lattice. This paper is mainly concerned with the situation in which C is the second dual ^4** of a complex Banach space A and, more particularly, when A is itself a JB* -triple. A subset %(A)õ f ^l(A**)~ consisting of the set %(A) of tripotents compact relative to A (denned in Section 4) with a greatest element adjoined is studied. It is shown to be an atomic complete lattice with the properties that the infimum of an arbitrary family of elements of %{A)~ is the same whether taken in % C (A)~ or in <%(A**)~ and that every decreasing net of non-zero elements of %(A)~ has a non-zero infimum. The relationship between the complete lattice %(A)~ and the complete lattice %(B)~, where B is a Banach space such that B** is a weak*-closed subtriple of A** is also investigated. When applied to the special case in which A is a C*-algebra the results provide information about the set of compact partial isometries relative to A and are closely related to those recently obtained by Akemann and Pedersen. In particular it is shown that a partial isometry is compact relative to A if and only if, in their terminology, it belongs locally to A. The main results are applied to this and other examples.
Pardaxin, an amphipathic polypeptide secreted by the Red Sea flatfish Pardachirus marmoratus whose sequence is NH2‐G‐F‐F‐A‐L‐I‐P‐K ‐I‐I‐S‐S‐P‐L‐F‐K‐T‐L‐L‐S‐A‐V‐G‐S‐A‐L‐S‐S‐S‐G‐G‐Q‐E, was synthesized by the solid‐phase method. The structure was verified by sequencing. The synthetic polypeptide changed the resistance of lipid bilayers by forming pores. At 10−7−10−8 M, the synthetic pardaxin increased the frequency of the spontaneous release of quanta of acetylcholine at the neuromuscular junction by up to 100‐fold, resembling the native product. Synthetic pardaxin seems to be a suitable tool for investigating the molecular structures underlying channel selectivity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.