Given a ®nitely supported sequence a on Z and an s s dilation matrix M, the transition operator Ta is the linear operator de®ned by Tav…a† :ˆ P b2Zs a…Maÿ b†v…b†, where a 2 Z and v lies in `0…Z†, the linear space of all ®nitely supported sequences on Z. In this paper we investigate the spectral properties of the transition operator Ta and apply these properties to the study of the approximation...

In this paper, we study skew (A,m)-symmetric operators in a complex Hilbert space H. Firstly, by introducing the generalized notion of left invertibility show that if T ? B(H) is (A,m)-symmetric, then eisT (A,m)-invertible for every s R. Moreover, examine some conditions (A,m)- symmetric to be (A,m?1)-symmetric. The connection between c0-semigroups (A,m)-isometries and (A,m)-symmetries also des...

For q ∈ (0, 1), let Bq denote the limit q-Bernstein operator. In this paper, the distance between Bq and Br for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 6 ‖Bq −Br‖ 6 2, where both of the equalities can be attained. To elaborate more, the distance depends on whether or not r and q are rational powers of each other. For example, if rj 6= qm for all j,...

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

We give an example of a non-compact, locally compact group G such that its Fourier–Stieltjes algebra B(G) is operator amenable. Furthermore, we characterize those G for which A * (G)—the spine of B(G) as introduced by M. Ilie and the second named author is operator amenable and show that A * (G) is operator weakly amenable for each G.

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

We prove the convergence in certain weighted spaces in momentum space of eigenfunctions of H = T − λV as the energy goes to an energy threshold. We do this for three choices of kinetic energy T , namely the nonrelativistic Schrödinger operator, the pseudorelativistc operator √ −∆+m2 − m, and the Dirac operator.

We give an example of a non-compact, locally compact group G such that its Fourier–Stieltjes algebra B(G) is operator amenable. Furthermore, we characterize those G for which A * (G)—the spine of B(G) as introduced by M. Ilie and the second named author—is operator amenable and show that A * (G) is operator weakly amenable for each G.