巴拿赫空间理论讲义 成人自考 (美)阿尔比亚克 新华正版
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作者(美)阿尔比亚克
出版社世界图书出版公司
ISBN9787510048043
出版时间2012-09
版次1
装帧平装
开本32
定价59元
货号xhwx_1200392069
上书时间2024-04-09
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内容简介：
thi book grew out of a oneemeter coure given by the econd author in 2001 and a ubequent twoemeter coure in 20042005， both at the univerity of miouricolumbia. the text i intended for a graduate tudent who ha already had a baic introduction to functional analyi; theaim i to give a reaonably brief and elfcontained introduction to claical banach pace theory.
banach pace theory ha advanced dramatically in the lat 50 year and we believe that the technique that have been developed are very powerful and hould be widely dieminated amongt analyt in general and not retricted to a mall group of peit. therefore we hope that thi book will alo prove of interet to an audience who may not wih to purue reearch in thi area but till would like to undertand what i known about the tructure of the claical pace.
claical banach pace theory developed a an attempt to anwer very natural quetion on the tructure of banach pace; many of thee quetion date back to the work of banach and hi chool in lvov. it enjoyed， perha， it golden period between 1950 and 1980， culminating in the definitive book by lindentrau and tzafriri [138] and [139]， in 1977 and 1979 repectively. the ubject i till very much alive but the reader will ee that much of the baic groundwork wa done in thi period.
at the ame time， our aim i to introduce the tudent to the fundamental technique available to a banach pace theorit. a an example， we pend much of the early chapter dicuing the ue of chauder bae and baic equence in the theory. the imple idea of extracting baic equence in order to undertand ubpace tructure ha bee econdnature in the ubject， and o the importance of thi notion i too eaily overlooked.
it hould be pointed out that thi book i intended a a text for graduate tudent， not a a reference work， and we have elected material with an eye to what we feel can be appreciated relatively eaily in a quite leiurely twoemeter coure. two of the mot pectacular dicoverie in thi area during the lat 50 year are enfio olution of the bai problem [54] and the gowermaurey olution of the unconditional baic equence problem [71]. the reader will find dicuion of thee reult but no preentation. our feeling， baed on experience， i that detouring from the development of the theory to preent lengthy and plicated counterexample tend to break up the flow of the coure. we prefer therefore to preent only relatively imple and eaily appreciated counterexample uch a the jame pace and tirelon pace. we alo decided， to avoid diruption， that ome counterexample of intermediate difficulty hould be preented only in the lat optional chapter and not in the main body of the text.
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