A closed subspace M in a Banach space X is called t/-proximinal if it satisfies: (1 + p)S n (S + M) ç S + e(pXS n M), for some positive valued function t(p), p > 0, and e(p) -» 0 as p -> 0, where 5 is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are (/-proximinal, for ...

LetM denote the maximal function along the polynomial curve (γ1t, . . . , γdt ): M( f )(x) = sup r>0 1 2r ∫ |t|≤r | f (x1 − γ1t, . . . , xd − γdt )|dt. We show that the L norm of this operator grows atmost logarithmically with the parameter d: ‖M f ‖L2(Rd) ≤ c log d ‖ f ‖L2(Rd), where c > 0 is an absolute constant. The proof depends on the explicit construction of a “parabolic” semi-group of op...

Let M and L be elliptic differential operators of orders 2m and 2/, respectively, with m ̂ S. The existence and uniqueness of a solution to the abstract mixed initial and boundary value problem Mu(t) + Lu(t) = 0, u(0) = u0 was established for u0 given in the domain of the infinitesimal generator of a strongly-continuous semi-group. The purpose of this paper is to show that this semi-group is hol...

In [24], Koliha proved that T ? L(X) (X is a complex Banach space) generalized Drazin invertible operator iff there exists an S commuting with such STS = and ?(T2S?T) {0} 0 < acc ?(T). Later, in [14, 34] the authors extended class of operators they also pseudo-Fredholm introduced by Mbekhta [27] other classes semi-Fredholm operators. As continuation these works, we introduce study 1zinvertib...

Abstract In the theory of approximation, linear operators play an important role. The exponential-type were introduced four decades ago, since then no new operator was by researchers, although several generalizations existing proposed and studied. Very recently, concept semi-exponential few captured from operators. It is more difficult to obtain than corresponding this paper, we extend studies ...

We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and corresponding pre-Hilbertian semi-norm ‖.‖φ on E such that ‖T (x)‖ ≤ 4 √ 2‖T‖ ‖x‖φ for all x ∈ E, is norm dense in the set of all bounded linear operators from E toH . As a tool for the above result, we show th...

The aim of this paper is to provide new upper bounds ω(T), which denotes the numerical radius a bounded operator T on Hilbert space (H,⟨·,·⟩). We show Aczél inequality in terms |T|. Next, we give certain inequalities about A-numerical ωA(T) and A-operator seminorm ∥T∥A an T. also present several results related 2×2 block matrices semi-Hilbert operators, by using symmetric matrices.