A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

Last time we discussed two main categories of linear models, and their combination. Here w t denotes a white noise: a stationary process with E w t = 0, E w 2 t = σ 2 , and E w t w s = 0 for s = t. MA(q) x t = µ + w t + q j=1 θ j w t−j = µ + w t + θ 1 w t−1 + · · · + θ q w t−q. x t is stationary with well-defined variance and covariances for any values of the coefficients θ 0 ,. .. , θ q , if q...

A unital C∗–algebra A is said to have the (APD)–property if every nonzero element in A has the approximate polar decomposition. Let J be a closed ideal of A. Suppose that J̃ and A/J have (APD). In this paper, we give a necessary and sufficient condition that makes A have (APD). Furthermore, we show that if RR(J ) = 0 and tsr(A/J ) = 1 or A/J is a simple purely infinite C∗–algebra, then A has (APD).

In this paper, we study 2-complex symmetric composition operators with the conjugation J, defined by Jf(z)=(f(z¯))¯, on Hardy space H2. More precisely, obtain necessary and sufficient condition for operator Cϕ to be J when ϕ is an automorphism of D. We also characterize a linear fractional self-map

Motivated by the idea of J-frame for a Krein space K , introduced by Giribet et al. (J. I. Giribet, A. Maestripieri, F. Martnez Peŕıa, P. G. Massey, On frames for Krein spaces, J. Math. Anal. Appl. (1), 393 (2012), 122–137.), we introduce the notion of ζ − J-tight frame for a Krein space K . In this paper we characterize J-orthonormal basis for K in terms of ζ−J-Parseval frame. We show that a K...