A Note on the Computable Categoricity of l(p) Spaces
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Computer Science—the theory, representation, processing, communication and use of information—is fundamentally transforming every aspect of human endeavor. The Department of Computer Science at Iowa State University advances computational and information sciences through; 1. educational and research programs within and beyond the university; 2. active engagement to help define national and international research, and 3. educational agendas, and sustained commitment to graduating leaders for academia, industry and government.
History
The Computer Science Department was officially established in 1969, with Robert Stewart serving as the founding Department Chair. Faculty were composed of joint appointments with Mathematics, Statistics, and Electrical Engineering. In 1969, the building which now houses the Computer Science department, then simply called the Computer Science building, was completed. Later it was named Atanasoff Hall. Throughout the 1980s to present, the department expanded and developed its teaching and research agendas to cover many areas of computing.
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1969-present
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- College of Liberal Arts and Sciences (parent college)
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Abstract
Suppose that p is a computable real and that p >= 1. We show that in both the real and complex case, l(p) is computably categorical if and only if p = 2. The proof uses Lamperti's characterization of the isometries of Lebesgue spaces of sigma-finite measure spaces.
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This is a manuscript of a proceeding published as McNicholl, T., A Note on the Computable Categoricity of l(p) Spaces, Evolving Computability, Proceedings of the 11th Conference on Computability in Europe, Lecture Notes in Computer Science, 9136 (2015): 268, doi: 10.1007/978-3-319-20028-6_27. Posted with permission. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-20028-6_27.