Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.

On a bounded strongly pseudo-convex domain X in C with a Lipschitz boundary, we prove that the ∂̄−Neumann operator N can be extended as a bounded operator from Sobolev (−1/2)−spaces to the Sobolev (1/2)−spaces. In particular, N is compact operator on Sobolev (−1/2)−spaces.

The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...

We present a simple smoothing operator for surfel-bounded solids obtained by adding two solids together using boolean operations. When adding two surfel-bounded solids together with the union operator, it is sometimes desirable to smooth out the sharp creases in the surface of the resulting solid. This report presents a simple local smoothing operator for this purpose. We illustrate that this o...

In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

We extend the concept of Lifshits–Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of (admissible) operators that are similar to self-adjoint operators. An operator H is called admissible if: (i) there is a bounded operator V with a bounded inverse such that H = V −1 HV for some self-adjoint operator H; (ii) the operators H and H are resolvent ...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...