Temat: \(k\)-symmetric points - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Some properties for \(\alpha\)-starlike functions with respect to \(k\)-symmetric points of complex order
Autorzy:: Darwish, H. E.
Lashin, A. Y.
Sowileh, S. M.
Powiązania:: https://bibliotekanauki.pl/articles/747047.pdf
Data publikacji:: 2017
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:: Analytic functions
starlike functions of complex order
convex functions of complex order
\(\alpha\)-starlike
\(k\)-symmetric points
subordination
Opis:: In the present work, we introduce the subclass \(\mathcal{T}_{\gamma ,\alpha}^{k}(\varphi )\), of starlike functions with respect to \(k\)-symmetric points of complex order \(\gamma\) (\(\gamma \neq 0\)) in the open unit disc \(\vartriangle\). Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.
Źródło:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 1
0365-1029
2083-7402
Pojawia się w:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals
Autorzy:: Czerwińska, Malgorzata M.
Kaminska, Anna H.
Powiązania:: https://bibliotekanauki.pl/articles/746224.pdf
Data publikacji:: 2017
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Symmetric spaces of measurable operators
unitary matrix spaces
rearrangement invariant spaces
k-extreme points
k-convexity
complex extreme points
complex convexity
monotonicity
(local) uniform (complex and real) convexity
p-convexity
Opis:: This is a review article of geometric properties of noncommutative symmetric spaces of measurable operators \(E(\mathcal{M},\tau)\), where \(\mathcal{M}\) is a semifinite von Neumann algebra with a faithful, normal, semifinite trace \(\tau\), and \(E\) is a symmetric function space. If \(E\subset c_0\) is a symmetric sequence space then the analogous properties in the unitary matrix ideals \(C_E\) are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and Pólya, Köthe duality, the spaces \(L_p\left(\mathcal{M},\tau\right)\), \(1\leq p < \infty\), the identification of \(C_E\) and \(G(B(H), \operatorname{tr})\) for some symmetric function space \(G\), the commutative case when \(E\) is identified with \(E(\mathcal{N}, \tau)\) for \(\mathcal{N}\) isometric to \(L_\infty\) with the standard integral trace, trace preserving \(*\)-isomorphisms between \(E\) and a \(*\)-subalgebra of \(E\left(\mathcal{M},\tau\right)\), and a general method for removing the assumption of non-atomicity of \(\mathcal{M}\). The main results on geometric properties are given in separate sections. We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, \(k\)-extreme points and \(k\)-convexity, (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec−Klee properties, Banach−Saks properties, Radon−Nikodym property and stability in the sense of Krivine−Maurey. We also state some open problems.
Źródło:: Commentationes Mathematicae; 2017, 57, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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