One of the main methods of examining non-normal operators, acting on Hilbert spaces, is the theory of contractions. This area of operator theory was developed by Béla Sz.-Nagy and Ciprian Foias from the dilation theorem of Sz.-Nagy. Sz.-Nagy and Foias classi ed the contractions according to their asymptotic behaviour. They got strong structural results in the case when the contraction and its a...

An important open problem in operator theory is the invariant subspace problem. Since the problem is solved for all finite dimensional complex vector spaces of dimension at least 2, H denotes a separable Hilbert space whose dimension is infinite. It is enough to think for a contraction T , that is, ‖T‖ ≤ 1 on H . Thus, T ( 6= 0) denotes a contraction in L(H). Let λ always denote an element of t...

The commutant lifting theorem of Sz.Nagy and Foiaş [22, 21] is a central result in the dilation theory of a single contraction. It states that if T ∈ B(H) is a contraction with isometric dilation V acting on K ⊃ H, and TX = XT , then there is an operator Y with ‖Y ‖ = ‖X‖, V Y = Y V and PHY = XPH. This result is equivalent to Ando’s Theorem that two commuting contractions have a joint (power) d...

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide wellestablished platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough s...

In this paper we present the relaxed inertial proximal algorithm for Ky Fan minimax inequalities. Based on Opial lemma, we propose a weak convergence result to a solution of the problem by eliminating in the algorithm (RIPAFAN) the Browder–Halpern’s factor of contraction. We present after, a first result of strong convergence by adding a strong monotonicity condition. Secondly, we eliminate the...

The semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model-theoretic point of view. A characterization of all revision schemes that satisfy the Gardenfors rationality postulates is given in terms of an ordering among interpretations. Properties of the contraction operator that can be defined in terms of revision are also studied. Two new up...

In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator Cn by an input/output logic. The results in this paper suggest that, in general, results f...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

In the recent preprint [1] S. Parrott proves the equality between the Arveson's curvature and the Fredholm index of a " pure " contraction with finite defect numbers. In the present note one derives a similar formula in the " non-pure " case. The notions of d-contraction T = (T 1 , T 2 ,. .. , T d) and its curvature was introduced by W. Arveson in a series of papers (see [2], [3], and [4]). In ...

Two level credibility-limited revision is a non-prioritized operation. When revising by two revision, levels of credibility and one incredibility are considered. sentence at the highest credibility, operator behaves as standard if second then outcome process coincides with contraction negation that sentence. If not credible, original belief set remains unchanged. In this paper, we propose const...