Abstract
We consider a generalization of the Pythagorean theorem with geometric meanings and from the generalization we were able to obtain a general and fundamental concept for the inversion of a family of bounded linear operators with continuous parameters on a Hilbert space into various Hilbert spaces. After reviewing the applications to linear mappings in the framework of Hilbert spaces of the general theory of reproducing kernels, we shall state the results for the case of operator versions. We shall consider solutions and generalized solutions of general bounded linear operator equations with continuous parameters on a Hilbert space.
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Saitoh, S. (2003). Reproducing Kernels and a Family of Bounded Linear Operators. In: Alpay, D. (eds) Reproducing Kernel Spaces and Applications. Operator Theory: Advances and Applications, vol 143. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8077-0_10
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DOI: https://doi.org/10.1007/978-3-0348-8077-0_10
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8077-0
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