the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan's theorem.

In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

In this paper we show that every power bounded operator weighted shift with commuting normal weights is similar to a contraction. As an application of this result, we reduce the problem whether every centered power bounded operator is similar to a contraction to the analogous question about quasi-invertible centered operators.

In this paper, we prove that the class of all generalized Drazin-Riesz invertible operators forms a regularity.

In this paper, we extend Jacobson's lemma for Drazin inverses to the generalized \(n\)-strong in a ring, and prove that \(1-ac\) is invertible if only \(1-ba\) invertible, provided \(a(ba)^{2}=abaca=acaba=(ac)^{2}a\). addition, left right Fredholm operators, furthermore, consistent invertibility spectral property index are investigated.

It is well-known that an operator in a finite-dimensional vector space is uniquely determined up to a similarity by its Jordan model. Given an operator T , two invariant subspaces M and N of T are said to be similar if there exists an invertible operator X such that XT = TX and XM = N . Clearly this is an equivalence relation in the lattice of invariant subspaces of T . Our paper was originally...

We give explicit representations of the generalized Drazin inverse of a block matrix having generalized Schur complement generalized Drazin invertible in Banach algebras. Also we give equivalent conditions under which the group inverse of a block matrix exists and a formula for its computation. The provided results extend earlier works given in the literature. 2010 Mathematics Subject Classific...