The paper is devoted to a general aggregation operator acting on L-fuzzy real numbers. It is defined as a t-norm based extension of an ordinary aggregation operator. The aim of our research is to analyze properties of the general aggregation operator depending on properties of the ordinary aggregation operator and the t-norm. By using the general aggregation operator we consider the properties ...

We study here how to reduce a t-norm by subtracting a value (computed by a function). We obtain a general form of an operator that we call the reduced t-norm. We study this operator and some interesting generalization properties. We also investigate some interesting particular cases. We complete the study by analyzing the dual operator, which corresponds to augmenting a t-conorms.

Last time, we proved that the noise operator Tα is hypercontractive. Recall that the noise operator Tαf is defined as (Tαf)(x) = Ey∼ x[f(y)] (1) where = 1−α 2 , and y ∼ x means that we choose yi to be xi with probability 1− and −xi with probability . We have also shown that it has Fourier expansion Tαf = ∑ S⊆[n] α f̂(S)χS . The hypercontractivity of the noise operator states that not only is the...

We estimate the essential norm of a weighted composition operator relatively to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space H∞ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.

We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of B(H) via a generalisation of a theorem of Stampfli. We show that for an elementary operator T of length `, the completely bounded norm is equal to the k-norm for k = `. A C*-algebra A has the property that the completely bounded norm of every elementary ope...

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...