We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...

This study recommends a GIS-based (Geographic Information Systems) and multi-criteria evaluation for site selection of gas power plant in Natanz City of Iran. The multi-criteria decision framework integrates legal requirements and physical constraints related to environmental and economic concerns. It also builds a hierarchy model for gas power plant suitability. The methodologies used for site...

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

In the present paper, we prove that the classical sets ∞(F ), c(F ), c0(F ) and p(F ) of sequences of fuzzy numbers are normed quasilinear spaces and the β−, α−duals of the set 1(F ) is the set ∞(F ). Besides this, we show that ∞(F ) and c(F ) are normed quasialgebras and an operator defined by an infinite matrix belonging to the class ( ∞(F ) : ∞(F )) is bounded and quasilinear. Finally, as an...

Abstract. Let T and V be two Hilbert space contractions and let X be a linear bounded operator. It was proved by C. Foias and J.P. Williams that in certain cases the operator block matrix R(X ;T, V ) (equation (1.1) below) is similar to a contraction if and only if the commutator equation X = TZ−ZV has a bounded solution Z. We characterize here the similarity to contractions of some operator ma...

A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT ∗C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ |T |, where J is an auxiliary conjugation commuting with |T | = √ T ∗T . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compr...

Given a Banach space operator with interior points in the localizable spectrum and without non-trivial divisible subspaces, this article centers around the construction of an infinite-dimensional linear subspace of vectors at which the local resolvent function of the operator is bounded and even admits a continuous extension to the closure of its natural domain. As a consequence, it is shown th...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator D ∈ B(X) is a Drazin inverse of T if TD = DT , D = TD and T k = T D for some nonnegative integer k. In this paper we look at the Jörgens algebra, an algebra of operators on a dual system, and characterise when an operator in that algebra has a Drazin inverse that is also in the algebra. This resu...

Abstract: This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included in the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. L2 robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear...

The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.