If a normalized Kähler-Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M , dimC M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.

Abu-Omar and Kittaneh [Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014), 521-527], wonder what is the smallest constant c such thatw(AB) ? c||A||w(B) all bounded linear operators A, B on a complex with A positive. Here, w(?) stands numerical radius. In this paper, we prove that = 3?3/4.

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

Let A be a linear bounded operator from a couple X = (X0, X1) to a couple Y = (Y0, Y1) such that the restrictions of A on the spaces X0 and X1 have bounded inverses. This condition does not imply that the restriction of A on the real interpolation space (X0, X1)θ,q has a bounded inverse for all values of the parameters θ and q. In this paper under some conditions on the kernel of A we describe ...

The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

In this paper, concept of fuzzy continuous operator, bounded linear operator are introduced in strong [Formula: see text]-b-normed spaces and their relations studied. Idea norm is developed completeness BF(X,Y) established.

and Applied Analysis 3 Recently, Marino and Xu 11 mixed the iterative method 1.6 and the viscosity approximation method 1.7 and considered the following general iterative method: xn 1 I − λnA Txn λnγf xn , n ≥ 0, 1.9 where A is a strongly positive bounded linear operator on H. They proved that if the sequence {λn} of parameters satisfies the following appropriate conditions: limn→∞λn 0, ∑∞ n 1 ...

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...