Recall some notations and terminology from [4]. For closed subspaces M, L of a Banach space X we write M e ⊂L (M is essentially contained in L ) if there exists a finite-dimensional subspace F ⊂ X such that M ⊂ L + F . Equivalently, dim M/(M ∩L) = dim(M + L)/L < ∞. Similarly we write M e =L if M e ⊂L and L e ⊂M . For a (bounded linear) operator T ∈ L(X) write R∞(T ) = ∞n=0 R(T) and N∞(T ) = ⋃∞ ...

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that followi...

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

We show that if Γ is an irreducible lattice in a higher rank center-free semi-simple Lie group with no compact factors and having property (T) of Kazhdan, then Γ is operator algebraic superrigid, i.e., any unitary representation of Γ which generates a II1 factor extends to a homomorphism of the group von Neumann algebra LΓ. This generalizes results of Margulis, and Stuck and Zimmer, and answers...

LetM denote the maximal function along the polynomial curve (γ1t, . . . , γdt ): M( f )(x) = sup r>0 1 2r ∫ |t|≤r | f (x1 − γ1t, . . . , xd − γdt )|dt. We show that the L norm of this operator grows atmost logarithmically with the parameter d: ‖M f ‖L2(Rd) ≤ c log d ‖ f ‖L2(Rd), where c > 0 is an absolute constant. The proof depends on the explicit construction of a “parabolic” semi-group of op...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

An algebra A of operators on a Banach space X is called strictly semitransitive if for all non-zero x, y ∈ X there exists an operator A ∈ A such that Ax = y or Ay = x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, LatA is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strict...

In this paper we study differentiability properties of the map T 7→ φ(T ), where φ is a given function in the disk-algebra and T ranges over the set of contractions on Hilbert space. We obtain sharp conditions (in terms of Besov spaces) for differentiability and existence of higher derivatives. We also find explicit formulae for directional derivatives (and higher derivatives) in terms of doubl...