In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...

In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on ∂D. This result is new even when S equals a single Toeplitz operator. Our main result can be used to prove, via a unified approach, several previously known results about compact Toeplitz oper...

The expansion of operators as ordered power series in the annihilation and creation operators a and a~ is examined. It is found that normally ordered power series exist and converge quite generally, but that for the case of antinormal ordering the required c-number coefficients are infinite for important classes of operators. A parametric ordering convention is introduced according to which nor...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

For unbounded operators t, s between Hilbert C*-modules which admit the polar decompositions V|t|, W|s|, respectively, we obtain an explicit upper bound estimate for the gap between t and s in terms of the norm of the bounded operators V − W , C|t| − C|s| and C|t∗| − C|s∗|, where C|t| and C|s| are the Cayley transforms of |t| and |s|. The result are used to drive a criterion for continuity of t...

If S(X ) ⊂ B(X ), where B(X ) denotes the algebra of operators on a Banach space X , then A ∈ B(X ) is S(X ) consistent if AB ∈ S(X ) ⇐⇒ BA ∈ S(X ) for every B ∈ B(X ). SVEP is a powerful tool in determining the S(X ) consistency of operators A for various choices of the subset S(X ).

Dedicated to Professor Shmuel Friedland. Abstract Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A1, . . . , Ak ∈ B(H) such that for any unitary operators U1, . . . , Uk, ∑k j=1 U ∗ j AjUj is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators. ...

In 1984 M. Putinar proved that hyponormal operators are subscalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S so that T ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this suffi...