A Characterization of C*-normed Algebras via Positive Functionals

We give a characterization of C*-normed algebras, among certain involutive normed ones. This is done through the existence of enough specific positive functionals. The same question is also examined in some non normed (topological) algebras.

A JORDAN-LIKE DECOMPOSITION IN THE NONCOMMUTATIVE SCHWARTZ SPACE

We show that every continuous self-adjoint functional on the noncommutative Schwartz space can be decomposed into a difference of two positive functionals. Moreover, this decomposition is minimal in the natural sense.

COMPLETELY POSITIVE MULTIPLIERS OF QUANTUM GROUPS

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group 𝔾 (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of 𝔾. It follows that there is an order bijection between the completely positive multipliers of L1(𝔾) and the positive functionals on the universal quantum group [Formula: see text]. We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak*–weak*-continuous.

Some Oscillation Results for Linear Hamiltonian Systems

The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian systemU′=A(t)U+B(t)V,V′=C(t)U−A∗(t)V. By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.