G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

We prove that for every bounded linear operator T : X → X, where X is a non-reflexive quotient of a von Neumann algebra, the point spectrum of T ∗ is non-empty (i.e. for some λ ∈ C the operator λI − T fails to have dense range.) In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into l∞ defined by

As an special intuitionistic fuzzy set defined on the real number set, triangular intuitionistic fuzzy number (TIFN) is a fundamental tool for quantifying an ill-known quantity. In order to model the decision maker's overall preference with mandatory requirements, it is necessary to develop some Bonferroni harmonic mean operators for TIFNs which can be used to effectively intergrate the informa...

In this paper, we introduce a special algebra called EQ-algebra which has three binary operations (meet, product, fuzzy equality) and a top element. The fuzzy equality is reflexive, symmetric and transitive with respect to the product. EQ-algebra is a natural algebra proposed as an algebra of truth values on the basis of which the fuzzy type theory (a higher-order fuzzy logic) should be develop...

Let Ai (i = 1,2, · · · ,k) be bounded linear operators on a Hilbert space. This paper aims to show a characterization of operator order Ak Ak−1 · · · A2 A1 > 0 in terms of operator inequalities. Afterwards, an application of the characterization is given to operator equalities due to Douglas’s majorization and factorization theorem. Mathematics subject classification (2010): 47A63.

We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator N that is similar to a Hilbert-Schmidt perturbation of a diagonal operator D is unitarily equivalent to a Hilbert-Schmidt perturbation of D; (2) For every normal operator A', diagonal operator D and bounded operator X, the Hilbert-Schmidt norms (finite or infinite) o...

Smooth implementation and controlling conflicting goals of a project with the usage of all related resources through organization is inherently a complex task to management. At the same time deterministic models are never efficient in practical project management (PM) decision problems because the related parameters are frequently fuzzy in nature. The project execution time is a major concern o...

Abstract. We study a factorization of bounded linear maps from an operator space A to its dual space A∗. It is shown that T : A −→ A∗ factors through a pair of a column Hilbert spaces Hc and its dual space if and only if T is a bounded linear form on A ⊗ A by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map ...

Environmental indices (EI) are common communication tool used to describe the overall status of environmental systems (e.g. air, water, soil). Development of EI entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. Ordered weighted averaging (OWA) operator is a general mean type operator that provides flexibility in the aggregation...