Functional Analysis in China

ISBN-13: 9789401065672 / Angielski / Miękka / 2013 / 376 str.

Bingren Li;Shengwang Wang;Shaozong Yan

Opis

Functional Analysis has become one of the main branches in Chinese mathematics. Many outstanding contributions and results have been achieved over the past sixty years.
This authoritative collection is complementary to Western studies in this field, and seeks to summarise and introduce the historical progress of the development of Functional Analysis in China from the 1940s to the present. A broad range of topics is covered, such as nonlinear functional analysis, linear operator theory, theory of operator algebras, applications including the solvability of some partial differential equations, and special spaces that contain Banach spaces and topological vector spaces. Some of these papers have made a significant impact on the mathematical community worldwide.
Audience: This volume will be of interest to mathematicians, physicists and engineers at postgraduate level.

Spis treści

Preface. Part One: Survey Papers. Some Problems and Results in the Study of Nonlinear Analysis; Shisheng Zhang. Topics on the Approximation Problem of Almost Isometric Operators by Isometric Operators; Guanggui Ding. Several Results on Nonsmooth Analysis; Xianling Fan. New Progress on Operator Semigroups and Linear Systems in Abstract Spaces; Dexing Feng. Some Results on Nonlinear Functional Analysis; Dajun Guo. Theory of Ba Spaces and Applications; Yuzan He, Peizhu Luo. On Completely Irreducible Operators; Chunlan Jiang, Shanli Sun. Multiplication of Distributions via Harmonic Representations; Banghe Li, Yaqui Li. C*-Crossed Products C(X)xalphaZ and C(X)xalphaZn with alphan = id; Bingren Li, Qing Lin. Advance of Operator Theory in Fudan University; Shaokuan Li, Xiaoman Chen. Some Aspects of Nonlinear Operators and Critical Point Theory; Shujie Li. Survey of Recent Progress in Non-Commutative Tori; Qing Lin. Some Results on the Structure of Toeplitz Operators; Shunhua Sun. Properties of Some Nonlinear Operators; Shengwang Wang. Embedding Properties of Locally Convex Riesz Spaces; Yau-chuen Wong. Advances of Research on Orlicz Spaces in Harbin; Congxin Wu, et al. Research on Some Topics of Banach Spaces and Topological Vector Spaces in Harbin; Congxin Wu. Some Results on Operator Algebra; Liangsen Wu. Operator Theory in Indefinite Inner Product Space; Shaozong Yan, Yusheng Tong. Random Metric Theory in China; Zhaoyong You, et al. Some Results on the Joint Spectrum for N-Tuple of Linear Operators; Dianzhou Zhang. Some Structural Properties of Banach Spaces; Junfeng Zhao. Part Two: Research Papers. The Plurisubharmonic Dentability and the Analytic Radon-Nikodym Property for Bounded Subsets in Complex Banach Spaces; Shangquan Bu. Existence of Entire Solutions of an Elliptic Equation on &mathR;N; Yanheng Ding, Shujie Li. All Liminal AF-Algebras are Stably Isomorphic to Finite AF-Algebras; Zhaobo Huang. The (U+K)-Orbit of Essentially Normal Operators and Compact Perturbation of Strongly Irreducible Operators; Youqing Ji, et al. The Complete Irreducibility of Analytic Toeplitz Operators; Chunlan Jiang, et al. Classification of Real Von Neumann Algebras (I); Bingren Li. C-Cosine Operator Functions and the Applications to the Second Order Abstract Cauchy Problem; Haiyan Wang, Shengwang Wang. Integrated Semigroups, Cosine Families and Higher Order Abstract Cauchy Problems; Tijun Xiao, Jin Liang. A Class of Toeplitz Operators on the Hardy Space; Kehe Zhu.