The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property...The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.展开更多
In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach spac...In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.展开更多
In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property.
A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the con...A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect展开更多
Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Rad...Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.展开更多
In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points ...In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.展开更多
SINCE Namioka and Phelps, starting with Asplund’s pioneering work, introduced the no-tion of Asplund spaces (those are Banach spaces on which every continuous convex function isFrechet differentiable on a dense G_δ ...SINCE Namioka and Phelps, starting with Asplund’s pioneering work, introduced the no-tion of Asplund spaces (those are Banach spaces on which every continuous convex function isFrechet differentiable on a dense G_δ subset) and proved that the dual of an Asplund space hasthe Radon-Nikodym property (RNP), the study of differentiability properties of functions oninfinite dimensional spaces has continued widely and deeply (see, for instance, Phelps andGiles). The research attained a great achievment after Stegall’s theorem: If the dualspace E~* has the RNP, then E is an Asplund space. Because of the N-Ph-S theorem, we展开更多
We show that a complex Banach space X has the analytic Radon-Nikodym property if and only if every non-empty closed bounded subset of X has a Jensen boundary point. If we suppose furthermore that X is isomorphic to it...We show that a complex Banach space X has the analytic Radon-Nikodym property if and only if every non-empty closed bounded subset of X has a Jensen boundary point. If we suppose furthermore that X is isomorphic to its square X2, X has the analytic Radon-Nikodym property if and only if every non-empty Jensen convex subset of X has a Jensen boundary poifit.展开更多
Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.
Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in prob...Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in probability) strongly.展开更多
文摘The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.
基金Project supported by the National Natural Science Foundation of Chinathe State Education Commission Ph. D. Station Foundation
文摘In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.
文摘In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property.
基金Project supported by the National Natural Science Foundation of China the Natural Science Foundation of Fujian Province of China.
文摘A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect
基金the National Natural Science Foundation of China,Grant No.10571035
文摘Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
基金Supported by the Research Institute of Fundamental Sciences, Tabriz, Iran.
文摘In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.
文摘SINCE Namioka and Phelps, starting with Asplund’s pioneering work, introduced the no-tion of Asplund spaces (those are Banach spaces on which every continuous convex function isFrechet differentiable on a dense G_δ subset) and proved that the dual of an Asplund space hasthe Radon-Nikodym property (RNP), the study of differentiability properties of functions oninfinite dimensional spaces has continued widely and deeply (see, for instance, Phelps andGiles). The research attained a great achievment after Stegall’s theorem: If the dualspace E~* has the RNP, then E is an Asplund space. Because of the N-Ph-S theorem, we
文摘We show that a complex Banach space X has the analytic Radon-Nikodym property if and only if every non-empty closed bounded subset of X has a Jensen boundary point. If we suppose furthermore that X is isomorphic to its square X2, X has the analytic Radon-Nikodym property if and only if every non-empty Jensen convex subset of X has a Jensen boundary poifit.
文摘Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.
基金Project supported by the National Natural Science Foundation of China
文摘Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in probability) strongly.
