cluster values of holomorphic functions of bounded type we study the cluster value theorem for hb x the frechet algebra of holomorphic functions bounded on bounded sets of x we also describe the size of fibers of the spectrum of hb x our results are rather complete whenever x has an unconditional shrinking basis and for x 1 as a byproduct we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of 1

envelopes of holomorphy and extension of functions of bounded type abstract we study the extension of holomorphic functions of bounded type defined on an open subset of a banach space to larger domains for this we first characterize the envelope of holomorphy of a riemann domain over a banach space with respect to the algebra of bounded type holomorphic functions in terms of the spectrum of the algebra we then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity we show that for bounded balanced sets extensions to the envelope are always of bounded type and that this does not necessarily hold for unbounded sets answering a question posed by hirschowitz in 1972 we also consider extensions to open subsets of the bidual present some banach stone type results and show some properties of the spectrum when the domain is the unit ball of l p

spectra of weighted lb algebras of entire functions on banach spaces abstract given a decreasing family of continuous weights on a banach space x we consider the weighted inductive limits of spaces of entire functions v h x and v h 0 x motivated by recent research by d carando and p sevilla peris on weighted frechet algebras of entire functions on banach spaces we determine conditions on the family of weights to ensure that the corresponding weighted space is an algebra or has polynomial schauder decompositions we study hormander algebras of entire functions defined on a banach space and we give a description of them in terms of sequence spaces we also focus on algebra homomorphisms between these spaces and obtain a banach stone type theorem for a particular decreasing family of weights finally we study the spectra of these weighted algebras endowing them with an analytic structure

on topological centre problems and sin quantum groups let a be a banach algebra with a faithful multiplication anda a be the quotient banach algebra of a with the left arens product we introduce a natural banach algebra which is a closed subspace of a a but equipped with a distinct multiplication with the help of this banach algebra new characteriza tions of the topological centre zt a a ofa a are obtained and a characterization of zt a a by lau and ulger for a having a bounded approximate identity is extended to all banach algebras the study of this banach algebra motivates us to introduce the notion of sin locally compact quantum groups and the concept of quotient strong arens irregularity we give characterizations of co amenable sin quan tum groups which are even new for locally compact groups our study shows that the sin property is intrinsically related to topological centre problems we also give characterizations of quotient strong arens irregularity for all quantum group algebras within the class of banach algebras introduced recently by the authors we characterize the unital ones generalizing the corresponding result of lau and ulger we study the interrelationships between strong arens irregularity and quotient strong arens irregularity revealing the complex nature of topological centre problems some open questions by lau and ulger on zt a a are also answered

properties and performance bounds for closed free choice synchronized monoclass queueing networks it is shown that many monoclass queuing networks qn with synchronizations can naturally be modeled with a subclass of petri nets pn called free choice nets fc for which a wide gamut of qualitative behavioral and structural results have been derived some of these net theoretic results are used to characterize the ergodicity boundedness and liveness of closed free choice synchronized qns upper and lower throughput bounds are defined based on the mean value of the service times without any assumption on the probability distributions thus including both the deterministic and the stochastic cases it is shown that monotonicity properties exist between the throughput bounds and the parameters of the model in terms of population and service times proposed are theoretically polynomial and practically linear complexity algorithms for the computation of these bounds based on linear programming problems defined on the incidence matrix of the underlying fc net using classical laws from queuing theory bounds are provided for mean queue lengths and response time

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

low complexity stochastic gradient pursuit algorithm and architecture for robust compressive sensing reconstruction compressive sensing cs is able to measure sparse signals with fewer measurements than nyquist rate the reconstruction of sparse signals in cs is an underdetermined problem for realistic applications the sparsity information may not be available the measurements are used to be disturbed by noise and efficient hardware realization is important existing cs reconstruction algorithms are tradeoff between noise tolerance and low complexity in this paper we propose a novel reconstruction algorithm called stochastic gradient pursuit sgp the stochastic gradient approach is applied to replace least square process of well known orthogonal matching pursuit omp algorithm since stochastic gradient approach iterates toward a minimum mean square error solution proposed algorithm shows robustness against noise furthermore proposed algorithm inherits the low complexity property of omp and shows feasibility of hardware implementation the sgp algorithm can achieve 36 higher success rate as well as 27 less complexity than omp when snr is 20 db finally we implement the algorithm with designed hardware sharing architecture in tsmc 90 nm technology the postlayout result shows that the core size is only 1 08 mm 2 at 150 mhz operation frequency compared with state of the art asic designs the proposed engine achieves 29 higher throughput to area ratio

the polynomial cluster value problem abstract the polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers we prove several polynomial cluster value theorems for uniform algebras h b between a u b and h b where b is the open unit ball of a complex banach space x we also obtain new results about the original cluster value problem especially for a b examples of spaces x considered here are spaces of continuous functions l 1 and locally uniformly convex spaces

spectra of weighted algebras of holomorphic functions we consider weighted algebras of holomorphic functions on a banach space we determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial schauder decompositions we study the spectra of weighted algebras and endow them with an analytic structure we also deal with composition operators and algebra homomorphisms in particular to investigate how their induced mappings act on the analytic structure of the spectrum moreover a banach stone type question is addressed

structure theory of equal conflict systems abstract equal conflict net systems are a weighted generalisation of the extended free choice subclass that keeps the total autonomy of choices a substantial part of the analytical branch of the structure theory of free choice systems including decomposition and duality the rank theorem characterisations of impartial sequences and prompt interfaces and the existence of home states is extended to the equal conflict case in so doing several familiar concepts and objects from the structure theory of place transition net systems are revisited from a linear algebraic perspective which is specially adequate to cope with weighted nets

superposition properties and performance bounds of stochastic timed event graphs this paper addresses the performance evaluation of stochastic timed event graphs the transition firing times are random variables with general distribution we first consider a stochastic timed event graph in which the firing times are generated by time superposition or addition of two sets of random variable sequences properties of this system are established chiefly we prove that the average cycle time is subadditive i e it is smaller than the sum of the average cycle times of the two stochastic timed event graphs in which the firing times are generated by one of the two sets of random variable sequences respectively based on these superposition properties we derive various upper bounds of the average cycle time of a general stochastic timed event graph in particular we obtain upper bounds which converge to the exact average cycle time as the standard deviations of the firing times decrease finally we derive performance bounds for stochastic timed event graphs with bounded firing times

octahedral norms and convex combination of slices in banach spaces abstract we study the relation between octahedral norms daugavet property and the size of convex combinations of slices in banach spaces we prove that the norm of an arbitrary banach space is octahedral if and only if every convex combination of w slices in the dual unit ball has diameter 2 which answers an open question as a consequence we get that the banach spaces with the daugavet property and its dual spaces have octahedral norms also we show that for every separable banach space containing l 1 and for every e 0 there is an equivalent norm so that every convex combination of w slices in the dual unit ball has diameter at least 2 e

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

cluster values for algebras of analytic functions abstract the cluster value theorem is known for being a weak version of the classical corona theorem given a banach space x we study the cluster value problem for the ball algebra a u b x the banach algebra of all uniformly continuous holomorphic functions on the unit ball b x and also for the frechet algebra h b x of holomorphic functions of bounded type on x more generally for h b u the algebra of holomorphic functions of bounded type on a given balanced open subset u x we show that cluster value theorems hold for all of these algebras whenever the dual of x has the bounded approximation property these results are an important advance in this problem since the validity of these theorems was known only for trivial cases where the spectrum is formed only by evaluation functionals and for the infinite dimensional hilbert space as a consequence we obtain weak analytic nullstellensatz theorems and several structural results for the spectrum of these algebras

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

automatic continuity of derivations on c algebras and jb triples abstract we introduce the notion of banach jordan triple modules and determine the precise conditions under which every derivation from a jb triple e into a banach jordan triple e module is continuous in particular every derivation from a real or complex jb triple into its dual space is automatically continuous motivating the study which we have carried out elsewhere of weakly amenable jb triples specializing to c algebras leads to a unified treatment of derivations and jordan derivations into modules shedding light on a celebrated theorem of barry johnson

solution of the contractive projection problem in this paper we show that the class of j algebras a class of concrete jordan triple systems is stable under the action of norm one projections this result constitutes a general solution to a problem considered by the authors and others specifically our main result is theorem 2 let p be an arbitrary contractive projection defined on a j algebra m then p m is a jordan triple system in the triple product a b c a b c p f ab c t cb a for a b c e p m and p m has a faithful representation as a j algebra

geometric characterization of tripotents in real and complex jb triples abstract we establish a geometric characterization of tripotents in real and complex jb triples as a consequence we obtain an alternative proof of kaup s banach stone theorem for jb triples

frechet algebras formal power series and analytic structure abstract the notion of locally riemann algebras is introduced by studying the ideal structure of frechet algebras we provide sufficient conditions for the existence of local analytic structure in the spectrum of a frechet algebra and as a welcome bonus we characterize locally riemann algebras

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

cluster values of analytic functions on a banach space we investigate uniform algebras of bounded analytic functions on the unit ball of a complex banach space we prove several cluster value theorems relating cluster sets of a function to its range on the fibers of the spectrum of the algebra these lead to weak versions of the corona theorem for l2 and for c0 in the case of the open unit ball of c0 we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in c 0

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

the daugavet property of c algebras jb triples and of their isometric preduals a banach space x is said to have the daugavet property if every rank one operator t x x satisfies id t 1 t we give geometric characterizations of this property in the settings of c algebras jb triples and their isometric preduals we also show that in these settings the daugavet property passes to ultrapowers and thus it is equivalent to an stronger property called the uniform daugavet property

fredholm composition operators on algebras of analytic functions on banach spaces we prove that fredholm composition operators acting on the uniform algebra h be of bounded analytic functions on the open unit ball of a complex banach space e with the approximation property are invertible and arise from analytic automorphisms of the ball

cycle time of stochastic event graphs evaluation and marking optimization addresses the performance evaluation and optimization of a strongly connected event graph with random firing times the authors proposed an upper bound and a lower bound for the average cycle time of event graphs knowing the initial marking the authors then prove that under some weak conditions on the firing time distributions it is possible to reach on average a cycle time smaller than any given value c with a finite marking assuming that c is greater than the greatest firing time finally the authors propose an heuristic algorithm to reach such an average cycle time while minimizing a p invariant criterion

homomorphisms and composition operators on algebras of analytic functions of bounded type abstract let u and v be convex and balanced open subsets of the banach spaces x and y respectively in this paper we study the following question given two frechet algebras of holomorphic functions of bounded type on u and v respectively that are algebra isomorphic can we deduce that x and y or x and y are isomorphic we prove that if x or y has the approximation property and h wu u and h wu v are topologically algebra isomorphic then x and y are isomorphic the converse being true when u and v are the whole space we get analogous results for h b u and h b v giving conditions under which an algebra isomorphism between h b x and h b y is equivalent to an isomorphism between x and y we also obtain characterizations of different algebra homomorphisms as composition operators study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on h b x with pathological behaviors

topological centers of module actions induced by unitary representations abstract in this paper we study the topological centers of bilinear maps induced by unitary representations giving a characterization when the center is minimal and also conditions which guarantee that the center is maximal various examples whose topological centers are maximal minimal or neither will be given we will also investigate the topological centers of sub representations direct sums and tensor products

interpolation sets and the size of quotients of function spaces on a locally compact group the research of the second author was partially supported by the spanish ministry of science including feder funds grant mtm2011 23118 and fundacio caixa castello bancaixa grant number p1 1b2014 35

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

analytic structure in fibers of h bc0 abstract let h b c 0 be the algebra of all bounded holomorphic functions on the open unit ball of c 0 and m h b c 0 the spectrum of h b c 0 we prove that for any point z in the closed unit ball of l there exists an analytic injection of the open ball b l into the fiber of z in m h b c 0 which is an isometry from the gleason metric of b l to the gleason metric of m h b c 0 we also show that for some banach spaces x b l can be analytically injected into the fiber m z h b x for every point z b x

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

aron berner extensions of triple maps with application to the bidual of jordan banach triple systems abstract by extending the notion of arens regularity of bilinear mappings we say that a bounded trilinear map on the cartesian product of banach spaces is aron berner regular when all its six aron berner extensions to the cartesian product of the bidual spaces coincide we give some results on the aron berner regularity of certain trilinear maps we then focus on the bidual e of a jordan banach triple system e and investigate those conditions under which e is itself a jordan banach triple system under each of the aron berner extensions of the triple product we also compare these six triple products with those arising from certain ultrafilters based on the ultrapower formulation of the principle of local reflexivity in particular we examine the aron berner triple products on the bidual of a jb triple in relation with the so called dineen s theorem some illuminating examples are included and some questions are also left undecided

representing measures and infinite dimensional holomorphy we consider some applications of the bishop de leeuw theorem about representing measures for some algebras of analytic functions on unit balls of banach spaces in particular we investigate hardy spaces h2 associated with corresponding algebras some examples are considered

on algebras of holomorphic functions of a given type we show that several spaces of holomorphic functions on a riemann domain over a banach space including the nuclear and hilbert schmidt bounded type are locally m convex frechet algebras we prove that the spectrum of these algebras has a natural analytic structure which we use to characterize the envelope of holomorphy we also show a cartan thullen type theorem

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

banach algebra structure and amenability of a class of matrix algebras with applications abstract we introduce a new category of banach algebras l 1 munn algebras which we use as a tool in the study of semigroup algebras then we characterize amenable l 1 munn algebras and also semisimple ones in this category applying these results to the semigroup algebras provides some characterizations of amenable semigroup algebras we also provide a counter example to a conjecture of duncan and paterson

isometries of real hilbert c modules abstract let t v w be a surjective real linear isometry between full real hilbert c modules over real c algebras a and b respectively we show that the following conditions are equivalent a t is a 2 isometry b t is a complete isometry c t preserves ternary products d t preserves inner products e t is a module map when a and b are commutative we give a full description of the structure of t

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

quasi completely continuous multilinear operators we introduce the concept of quasi completely continuous multilinear operators and use this concept to characterize for a wide class of banach spaces x1 xk the multilinear operators t x1 xk x with an x valued aron berner extension

arens regularity and local reflexivity principle for banach algebras on considere les proprietes des produits de arens et le produit j u en particulier la w continuite on montre qu un automorphisme un antiautomorphisme un multiplicateur de e peuvent etre etendus a e j u avec la meme propriete

topological centers of certain dual algebras let a be a banach algebra with a bounded approximate identity let z1 and z2 be respectively the topological centers of the algebras a and a a in this paper for weakly sequentially complete banach algebras in particular for the group and fourier algebras l1 g and a g we study the sets z1 z2 the relations between them and with several other subspaces of a or a

a characterization of the closed unital ideals of the fourier stieltjes algebra b g of a locally compact amenable group g abstract let g be a locally compact amenable group b g its fourier stieltjes algebra and i be a closed ideal of it in this paper we prove the following result the ideal i has a unit element iff it is principal this is the noncommutative version of the glicksberg host parreau theorem the paper also contains an abstract version of this theorem

module maps on duals of banach algebras and topological centre problems we study various spaces of module maps on the dual of a banach algebra a and relate them to topological centres we introduce an auxiliary topological centre zt a a for the left quotient banach algebra a a of a our results indicate that zt a a is indispensable for investigating properties of module maps over a and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different arens irregularity properties for the class of banach algebras of type m introduced recently by the authors we show that strong arens irregularity can be expressed both in terms of automatic normality of a module maps on a and through certain commutation relations this in particular generalizes the earlier work on group algebras by ghahramani and mcclure 1992 13 and by ghahramani and lau 1997 12 we link a module map property over a to the space wap a of weakly almost periodic functionals on a generalizing a result by lau and ulger 1996 34 for banach algebras with a bounded approximate identity we also show that for a locally compact quantum group g the quotient strong arens irregularity of l1 g can be obtained from that of m g and can be characterized via the canonical c0 g module structure on luc g

hardy type spaces associated with compact unitary groups abstract we investigate hilbertian hardy type spaces of complex analytic functions of infinite many variables associated with compact unitary groups and the corresponding invariant haar s measures for such analytic functions we establish a cauchy type integral formula and describe natural domains also we show some relations between constructed spaces of analytic functions and the symmetric fock space

on a conjecture by ghahramani lau and related problems concerning topological centres abstract let a be a banach algebra and consider a equipped with the first arens product we establish a general criterion which ensures that a is left strongly arens irregular i e the first topological centre of a is reduced to a itself using this criterion we prove that for a very large class of locally compact groups ghahramani lau s conjecture cf lau 94 and gha lau 95 stating the left strong arens irregularity of the measure algebra m g holds true our methods obviously yield as well the right strong arens irregularity in the situation considered furthermore the same condition used above implies that every linear left a module homomorphism on a is automatically bounded and w continuous we finally show that our criterion also yields a partial answer to a question raised by lau ulger trans amer math soc 348 3 1996 1191 on the topological centre of the algebra a a for a having a right approximate identity bounded by 1

module homomorphisms and topological centres associated with weakly sequentially complete banach algebras abstract this paper is a contribution to the theory of weakly sequentially complete banach algebras a we require them to have bounded approximate identities and for the most part to be ideals in their second duals so that examples are the group algebras l 1 g for compact groups g or the fourier algebras a g for discrete amenable groups g in section 2 we present our main result that the topological centre or set of weak bicontinuous elements of a is identifiable with a as a corollary we deduce in section 3 that each left a module homomorphism from a to a a can be realized as right translation by an element of a these conclusions generalise recent advances in the subject in section 4 we take a special algebra l 1 s for a commutative discrete semigroup s and show that if its second dual has an identity then that identity must lie in l 1 s

tingley s problem through the facial structure of an atomic jbw triple abstract we prove that every surjective isometry between the unit spheres of two atomic jbw triples e and b admits a unit extension to a surjective real linear isometry from e into b this result constitutes a new positive answer to tingley s problem in the jordan setting

real contractive projections on commutative c algebras complex banach jordan triples occurred in the study of bounded symmetric domains in several complex variables and in the study of contractive projections on complex c algebras these spaces are equipped with a ternary product the jordan triple product and are essentially geometric objects in that the linear isometries between them are exactly the linear maps preserving the triple product 13

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

isometric isomorphisms between banach algebras related to locally compact groups let g1 g2 be locally compact groups we prove in this paper that if t is an isometric isomorphism from the banach algebra luc g1 the continuous dual of the banach space of left uniformly continuous functions on g1 equipped with arens multiplication onto luc g2 i then t maps m g1 onto m g2 and li g onto l g2 we also prove that any isometric isomorphism from li g second conjugate algebra of l gi onto ll g2 maps l g1 onto l g2 0 introduction and preliminaries let g1 g2 be locally compact groups let m gi i 1 2 be the banach algebra of regular borel measures on gi a well known result of b e johnson 10 asserts that if t is an isometric isomorphism from m g1 onto m g2 then t maps ll g onto l g2 and hence g1 and g2 must be isomorphic by wendel s theorem 21 in this paper we prove theorem 3 1 c among other things that if t is an isometric isomorphism from ll g1 onto l1 g2 then t maps l1 g1 onto ll g2 this answers affirmatively a question raised in 4 theorem 3 1 c was proved for abelian locally compact groups by lau and losert in 13 and for compact and discrete groups by ghahramani and lau in 4 let g be a locally compact group let c g denote the space of bounded continuous complex valued functions on g with the sup norm topology and luc g denote the closed subspace of bounded left uniformly continuous functions on g i e all f e c g such that the map x lxf from g into c g is continuous where lxf y f xy x y e g then luc g is a banach algebra with the arens multiplication defined by nm f n m1f n m e luc g f e luc g where mlf x m lxf x e g furthermore m g may be identified with a closed subspace of luc g by the natural embedding u f f f x du x f e luc g u e m g it was received by the editors november 1 1988 1980 mathematics subject classification 1985 revision primary 43a20

orthogonally additive polynomials on spaces of continuous functions we show that for every orthogonally additive homogeneous polynomial p on a space of continuous functions c k with values in a banach space y there exists a linear operator s c k y such that p f s f n this is the c k version of a related result of sundaresam for polynomials on l p spaces

the spectrum of analytic mappings of bounded type abstract a banach space e is said to be symmetrically regular if every continuous symmetric linear mapping from e to e is weakly compact for a complex banach space e and a complex banach algebra f let h b e f denote the algebra of holomorphic mappings from e to f which are bounded on bounded sets we endow h b e f with the usual frechet topology m h b e f f denotes the set of all non null continuous homomorphisms from h b e f to f a subset of g ef on which the extension of zalduendo is multiplicative is presented and it is shown that in general the sets g ef and m h b e f f do not coincide we prove that if e is symmetrically regular and every continuous linear mapping from e to f is weakly compact then there exists an analytic structure on m h b e f f

on the zelmanovian classification of prime jb triples complex jb triples are complex banach spaces endowed with a triple product subjected to suitable conditions of algebraic and analytic nature see section 1 for the definition they were introduced by w kaup in order to provide an algebraic setting for the study of bounded symmetric domains in complex banach spaces the open unit ball of every complex jb triple is a bounded symmetric domain ka1 and every bounded symmetric domain in any complex banach space is bi holomorphically equivalent to the open unit ball of a suitable complex jb triple ka3 fundamental examples of complex jb triples are provided by complex c algebras with triple product defined by xyz x 1 2 xy z zy x 1

little grothendieck s theorem for real jb triples we prove that given a real jb triple e and a real hilbert space h then the set of those bounded linear operators t from e to h such that there exists a norm one functional varphi in e and corresponding pre hilbertian semi norm varphi on e such that