suppose $t$ and $s$ are moore-penrose invertible operators betweenhilbert c*-module. some necessary and sufficient conditions are given for thereverse order law $(ts)^{ dag} =s^{ dag} t^{ dag}$ to hold.in particular, we show that the equality holds if and only if $ran(t^{*}ts) subseteq ran(s)$ and $ran(ss^{*}t^{*}) subseteq ran(t^{*}),$ which was studied first by greville [{it siam rev. 8 (1966...

We present a design of a module system for C++, along with rationale for the design choices. The document focuses on programmer’s view of modules (both production and consumption) and how to better support modular programming in the large, componentization, scalable compilation, and semantics-aware developer tools.

We present a design of a module system for C++, along with rationale for the design choices. The document focuses on programmer’s view of modules (both production and consumption) and how to better support modular programming in the large, componentization, scalable compilation, and semantics-aware developer tools.

We show that every infinite-dimensional commutative unital C∗-algebra has a Hilbert C∗-module admitting no frames. In particular, this shows that Kasparov’s stabilization theorem for countably generated Hilbert C∗-modules can not be extended to arbitrary Hilbert C∗-modules.

41 Elementary Number Theory 92 41.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 92 41.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 92 41.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 93 41.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 96 41.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 97 4...

In this paper we view some fundamentals of the theory of Hilbert C-modules and examine some ways in which Hilbert C-modules differ from Hilbert spaces. ∗2000 Mathematics Subject Classification. 46L08.

Abstract. We consider a class of C-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner’s Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are K-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product b...

We present a design of and a specification of module system for C++. The proposal focuses on programmer’s view of modules (both production and consumption) and how to better support modular programming in the large, componentization, scalable compilation, and semantics-aware developer tools.