Innovation is widely recognized as a key factor in the competitiveness of nations and firms. Small firms that do not embrace innovation within their core business strategy run the risk of becoming uncompetitive because of obsolete products and processes. Innovative firms are a perquisite for a dynamic and competitive economy.This paper reports on the results of a study that examined barriers to firm innovation among a sample of 294 managers of small and medium-sized enterprises (SMEs) in Spain. The study examined the relation between (1) product, process, and management innovation and (2) 15 obstacles to innovation, which can limit a firm's ability to remain competitive and profitable. Findings of the study show that barriers have a differential impact on the various types of innovation; product, process, and management innovation are affected differently by the different barriers. The most significant barriers are associated with costs, whereas the least significant are associated with manager/employee resistance. Additionally, the results demonstrate that the costs associated with innovation have proportionately greater impact on small than on larger firms.The findings can be used in the development of public policy aimed at supporting and encouraging the innovation among SMEs in Spain. Government policies that encourage and support innovation among all firms, especially small firms, can help countries remain competitive in a global market. Public policy that encourages innovation can enable firms to remain competitive and survive, both of which have

We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás theorem holds for operators from 1 into Y . Several examples of classes of such spaces are provided. For instance, the Bishop-Phelps-Bollobás theorem holds when the range space is finite-dimensional, an L 1 (μ)-space for a σ -finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.

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It is shown that for every quasi-normed ideal Q of n-homogeneous continuous polynomials between Banach spaces there is a quasi-normed ideal A of n-linear continuous mappings A such that q ∈ Q if and only if the associated n-linear mappingq of q is in A.

Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series a n /n s , s ∈ C, converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr's strip for a Dirichlet series with coefficients a n in Y is bounded by 1 − 1/ Cot(Y ), where Cot(Y ) denotes the optimal cotype of Y . This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series. Mathematics Subject Classification (2000)Primary 32A05; Secondary 46B07 · 46B09 · 46G20 The first, second and third authors were supported by MEC and FEDER Project MTM2005-08210. A. Defant