ACTA SCIENTIARUM MATHEMATICARUM最新文献

Let X be an infinite-dimensional complex Banach space and let (mathcal {B}(X)) denote the algebra of all bounded linear operators on X. For an operator (T in mathcal {B}(X)) the sets (sigma _{1}(T), sigma _{2}(T),) and (sigma _{3}(T)) are called, respectively, the semi-Fredholm domain, the Fredholm domain, and the Weyl domain, of T in the spectrum, (sigma (T)). Given (i in {1,2,3}), the goal of this article is to describe the general form of all surjective maps (phi ) on (mathcal {B}(X)) which satisfy

for all (A, T in mathcal {B}(X)).

In this paper, we define the new concept of (E_{f,g})-contraction mapping and check common fixed point theorems for such contractions in metrically convex metric spaces. We provide an example to support the presented results.

This paper deals with a weaker form of the property so called ({textbf {L}}_{o,o}) for operators, which we call the property weak ({textbf {L}}_{o,o}) for operators. We characterize this property in terms of convergence of approximate norm attainment sets and prove that a pair of Banach spaces (X, Y) satisfies the property weak ({textbf {L}}_{o,o}) for compact operators if and only if X is reflexive. We further investigate the property weak ({textbf {L}}_{o,o}) for bilinear maps and obtain a connection of it with the property weak ({textbf {L}}_{o,o}) for operators. Importantly, we also characterize some geometric properties of Banach spaces with the help of convergence of approximate norm attainment sets.

Let n be a positive integer and H a Hilbert space. The description of the general form of bijective maps on the set of n-dimensional subspaces of H preserving the maximal principal angle has been obtained recently. This is a generalization of Wigner’s unitary-antiunitary theorem. In this paper we will obtain another extension of Wigner’s theorem in which the maximal principal angle is replaced by the minimal one. Moreover, in this case we do not need the bijectivity assumption.

We consider pure quartic relative extensions of the number field ({{mathbb {Q}}}(i)) of type (K={{mathbb {Q}}}(root 4 of {a+bi})), where (a,bin {{mathbb {Z}}}) and (bne 0), such that (a+biin {{mathbb {Z}}}[i]) is square-free. We describe integral bases of these fields. The index form equation is reduced to a relative cubic Thue equation over ({{mathbb {Q}}}(i)) and some corresponding quadratic form equations. We consider monogenity of K and relative monogenity of K over ({{mathbb {Q}}}(i)). We shall show how our former method based on the factors of the index form can be used in the relative case to exclude relative monogenity in some cases.

We consider countable extensions of commutative and unital Banach algebras. We study these Banach algebra structures with or without assuming the continuity of the canonical injection. We also prove that a countable extension endowed with a Banach algebra norm with continuous injection is actually a finite extension.

An element ((x_1, ldots , x_n)in E^n) is called a norming point of (Tin {{mathcal {L}}}(^n E)) if (Vert x_1Vert =cdots =Vert x_nVert =1) and (|T(x_1, ldots , x_n)|=Vert TVert ,) where ({{mathcal {L}}}(^n E)) denotes the space of all continuous n-linear forms on E. For (Tin {{mathcal {L}}}(^n E),) we define

Let ({mathbb {R}}^2_{h(w)}) denote the plane with the hexagonal norm with weight (0<w<1)

We classify (text {Norm}(T)) for every (Tin {{mathcal {L}}}(^2 {mathbb {R}}_{h(w)}^2)).

We find sufficient conditions for a self-map of the unit ball to converge uniformly under iteration to a fixed point or idempotent on the entire ball. Using these tools, we establish spectral containments for weighted composition operators on Hardy and Bergman spaces of the ball. When the compositional symbol is in the Schur–Agler class, we establish the spectral radii of these weighted composition operators.