000			02023nam a2200193 4500
001			4521709
010			_a 99025273
020			_a1852331585 (acidfree paper)
082	0	0	_a515.98 _bDIN/C
100	1		_aDineen, Seán
245	1	0	_aComplex analysis of infinite dimensional spaces
260			_aLondon _aNew York _bSpringer _c1999
300			_axv, 543 p.
520			_aInfinite dimensional holomorphy is the study of holomorphic or analytic func­ tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself ini­ tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suit­ able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.
650		0	_aHolomorphic functions
650		0	_aLinear topological spaces
650		0	_aFunctions of complex variables
942			_cBK
999			_c66953 _d66953