Search Results

You are looking at 1 - 10 of 62 items :

Clear All

Abstract

Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception, since it could hinder making headway in this already hard enough subject. To that end we show that Bayoumi quasi-differentiability, when properly defined, is the same as Fréchet differentiability, and that some of his alleged applications are wrong.

Abstract

We prove that if Köthe F-spaces X and Y on finite atomless measure spaces (ΩX; ΣX, µX) and (ΩY; ΣY; µY), respectively, with absolute continuous norms are isomorphic and have the property $\mathop {\lim }\limits_{\mu (A) \to 0} \left\| {\mu (A)^{ - 1} 1_A } \right\| = 0$ (for µ = µX and µ = µY, respectively) then the measure spaces (ΩX; ΣX; µX) and (ΩY; ΣY; µY) are isomorphic, up to some positive multiples. This theorem extends a result of A. Plichko and M. Popov concerning isomorphic classification of L p(µ)-spaces for 0 < p < 1. We also provide a new class of F-spaces having no nonzero separable quotient space.

Abstract

We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.

Abstract

We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex

need not to be convex. For any x G X, let d(x, C) = 1991 Mathematics Subject Classification: 41A50, 54H25, 47H10, 46A16. Key words and phrases: best C-approximants, common fixed point, commuting maps, locally G-contractive map, locally G-nonexpansive map, p-normed space. 832 L. A. Khan, A. Latif in f Z ecd (x , z ) , and let Pc(x) := {x € C : d(x,x) = d(x,C)}, the set of best C-approximants to x. Pc(x) is always a bounded subset of X and it is closed or convex if C is so [1]. Now we adopt the following definitions for convenience. Let G be a family of single

FREE ACCESS

Miroslav Pavlović Function Classes on the Unit Disc De Gruyter Studies in Mathematics | Edited by Carsten Carstensen, Berlin, Germany Gavril Farkas, Berlin, Germany Nicola Fusco, Napoli, Italy Fritz Gesztesy, Waco, Texas, USA Niels Jacob, Swansea, United Kingdom Zenghu Li, Beijing, China Karl-Hermann Neeb, Erlangen, Germany Volume 52 Miroslav Pavlović Function Classes on the Unit Disc | An Introduction 2nd edition Mathematics Subject Classification 2010 46E10, 46E15, 46E30, 30H10, 30H20, 30H25, 30H30, 30H35, 31A05,31C45,30J05, 30J15, 30C62, 30C55, 46A16, 47B33

earlier paper [3] in which we have studied, in the non-locally convex framework, multiplication operators on weighted function spaces which are induced by scalar- and vector-valued mappings. The purpose of this paper is to characterize those multiplication opera- tors which are induced by operator-valued mappings. These results extend, 1991 Mathematics Subject Classification: 47B38, 46E40, 46A16. Key words and phrases: Nachbin family of weights, topological vector spaces, weighted topology, multiplication operators. 600 L. A. Khan, Α. Β. Thaheem in particular

¬n khràkvn, nicht Kyrik¬n. 46.8. Strathgåw t¬n Mak(edÞnvn). 43.16. Könnte der Mann nicht auch Stratege von Makedonia und Adrianupolis gewesen sein, so wie 46.A.16? 46.15. Theophilos war Protonotar des Themas Makedonia. 47.4. Das Siegel des Pakratios als Kleisuriarch von Mesembria ist sicher deutlich nach 917 zu datieren, demgemäß nach 971. 47.d. Das im Kommentar zu ‰k prosqpoy MeshmbrÝaw unter Nr. 4 angeführte Siegel eines Kyriakos bietet spauarokandid¯tow ‰pä to® XrysotriklÝnoy, nicht ‰pä to® magglabÝoy; bei Nr. 5 ziehen wir immer noch den Vornamen Himerios vor. 47

.002(1) *0.005(2) 0.017(1) C(52) 16f *0.00488(6) 0.32260(6) 0.9280(3) 0.038(1) 0.037(1) 0.051(2) 0.006(1) 0.004(1) 0.012(1) Table 3. Atomic coordinates and displacement parameters (in Å2). Atom Site x y z U11 U22 U33 U12 U13 U23 H(38) 16f *0.1018 0.3938 0.5963 0.046 H(41) 16f *0.0641 0.3429 0.4971 0.048 H(42) 16f *0.0217 0.3069 0.4314 0.057 H(43) 16f 0.0321 0.3116 0.5136 0.051 H(44) 16f 0.0443 0.3526 0.6677 0.036 H(46A) 16f 0.0289 0.3768 0.9103 0.030 Table 2. continued. Atom Site x y z Uiso H(46B) 16f 0.0023 0.4019 0.9708 0.030 H(48) 16f *0.0566 0.3805 1.0086 0.044 H(49

.2 26.7 15.3 41 ,9 13.0 50.9 128.3 60.3 23.3 58.'. 44.7 68.0 10.9 63.a 46.a 16.1 16.2 61.2 19.2 -16.0 -39.4 -36.2 -50.0 11.2 126.2 - 4.6 22.6 -36.8 -B1.8 57.4 32.2 -40,6 -46.0 6.4 -162.0 -54.6 60.0 53.2-28.6 - 1.0 -15.4 -30.4 1.6 31.4 -72.6 51.2 11.0 -33.4 -56.0 -65.4 52.2 35.8 7.4 -32.8 -53.2 -58.8 11 .0 9.8 -34.4 -20.2 16.0 -29.0 9.4 -10.4 44.4 - 2.0 -51.8 - 5.4 28.0 45.4 83,6 -96.O -45.0 - 1.2 154.4 - 3.B 118.4 15.4 -112.4 -74.0 37.2 10.8 85.426.4 10.2 -12.2 -27.6 - 3.0 -32.6 10.8 -11.2 -12.4 -44.0 12.8 -51.6 5-8 141.4 52.0 -23.0 54.6 -49-0 65.8 11.8 -62.6 53.8 -16