In this paper, we give theoretical results on Macaev ideal and Dixmier trace. Then we give a characterization of antiholomorphic symbols \overline f such that the Hankel operator {H_{\overline f }} on a Bergman weighted space is in an ideal of Macaev and we give the Dixmier trace. For this, we look at the behavior of Schatten’s norms \mathcal{S}^p when p tends to 1, using results of Engliš and Rochberg on Bergman space. We also give results on powers of such operators., Nous donnons des résultats théoriques sur l’idéal de Macaev et la trace de Dixmier. Ensuite, nous caractérisons les symboles antiholomorphes \overline f tels que l’opérateur de Hankel {H_{\overline f }} sur l’espace de Bergman à poids soit dans l’idéal de Macaev et nous donnons la trace de Dixmier. Pour cela, nous regardons le comportement des normes de Schatten \mathcal{S}^p quand p tend vers 1 et nous nous appuyons sur le résultat de Engliš et Rochberg sur l’espace de Bergman. Nous parlons aussi des puissances de tels opérateurs., Romaric Tytgat., and Obsahuje seznam literatury
This paper argues, in essence, that toli, a gbe dialect spoken in Benin, has two underlying tones: high and low. All other tones are derived from these basic tones, as demonstrated by numerous examples in the article.
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space., Songxiao Li, Ruishen Qian, Jizhen Zhou., and Obsahuje bibliografické odkazy
Let $\varphi $ and $\psi $ be holomorphic self-maps of the unit disk, and denote by $C_\varphi $, $C_\psi $ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_\varphi -C_\psi $ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator $C_{\varphi }$, when $\varphi $ is a linear-fractional self-map of $\mathbb {D}$. In this paper first, we investigate the essential normality problem for the operator $T_{w}C_{\varphi }$ on the Hardy space $H^{2}$, where $w$ is a bounded measurable function on $\partial \mathbb {D}$ which is continuous at each point of $F(\varphi )$, $\varphi \in {\cal S}(2)$, and $T_{w}$ is the Toeplitz operator with symbol $w$. Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on $H^{2}$.
Let K ⊂ ℝm (m ≥ 2) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C(1) 0 be the class of all continuously differentiable real-valued functions with compact support in m and denote by σm the area of the unit sphere in m. With each ϕ ∈ C(1) 0 we associate the function WKϕ(z) = 1⁄ σm ∫ Rm\K grad ϕ(x) · z − x |z − x| m dx of the variable z ∈ K (which is continuous in K and harmonic in K \ B). WKϕ depends only on the restriction ϕ|B of ϕ to the boundary B of K. This gives rise to a linear operator WK acting from the space C(1)(B) = {ϕ|B; ϕ ∈ C(1) 0 } to the space C(B) of all continuous functions on B. The operator TK sending each f ∈ C(1)(B) to TKf = 2WKf − f ∈ C(B) is called the Neumann operator of the arithmetical mean; it plays a significant role in connection with boundary value problems for harmonic functions. If p is a norm on C(B) ⊃ C(1)(B) inducing the topology of uniform convergence and G is the space of all compact linear operators acting on C(B), then the associated p-essential norm of TK is given by ωpTK = inf Q∈G sup {p[(TK − Q)f]; f ∈ C(1)(B), p(f) ≤ 1} . In the present paper estimates (from above and from below) of ωpTK are obtained resulting in precise evaluation of ωpTK in geometric terms connected only wit K.
This paper mainly addresses the relation between essentialism and philosophical method. In particular, our analysis centers on the anti-essentialist argument that proposed, given its essentialist bonds, the abandonment of the notion of method. To this end, we make use of the empirical evidence concerning essentialism provided by psychological research, which has shown that our proneness to essentialize is not a by-product of our social and cultural practices as some anti-essentialists have thought. Rather, it is a deeply rooted cognitive tendency that plays a major role in concept formation and so in our understanding of things. Thus, given that such inclination toward essentialism is certain to happen, we argue for a conception of method that, while not overcoming such tendency, avoids the presumed disastrous consequences feared by most anti-essentialists., Tento příspěvek se zabývá především vztahem mezi esencialismem a filozofickou metodou. Konkrétně se naše analýza soustřeďuje na argument anti-esencialismu, který s ohledem na esenciální vazby navrhoval opuštění pojmu metody. Za tímto účelem využíváme empirických důkazů o esencialismu poskytovaném psychologickým výzkumem, který ukázal, že naše snaha o esencializaci není vedlejším produktem našich sociálních a kulturních praktik, jak si mysleli někteří anti-esenciologové. Spíše je to hluboce zakořeněná kognitivní tendence, která hraje důležitou roli při tvorbě konceptu a tak v našem chápání věcí. Vzhledem k tomu, že takový náklon k esencialismu se jistě stane, argumentujeme za koncepci metody, která, aniž by tuto tendenci překonala., and Fernando E. Vásquez Barbra
From the perspective of the concept of aesthetic synthesis, i.e. the principle of the internal organization of works of art, this study looks at the question of the linkage of works of art and the possibility of social reconciliation in the thought of Theodor W. Adorno. The starting point of the interpretation consists of two passages from Aesthetic Theory. Subsequently, the meaning of Adorno’s concept of aesthetic synthesis as a principle open to the peculiar is clarified. This is also where the social significance of the aesthetic synthesis of works of art originates as a reference or reminder of the possibility of social change. and Tato studie nahlíží na otázku vazby uměleckých děl a možnosti společenského smíření v myšlení Theodora W. Adorna z perspektivy pojmu estetické syntézy, tj. principu vnitřní organizace uměleckých děl. Východiskem interpretace jsou dvě pasáže z Estetické teorie. Následně je objasněn význam Adornova pojetí estetické syntézy coby principu otevřeného vůči zvláštnímu. Odtud pramení také sociální význam estetické syntézy uměleckých děl jakožto poukazu či upomínky na možnost společenské změny.