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2005ā€¢Annales mathĆ©matiques Blaise PascalOpen access

Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications

Toka Diagana

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Abstract

We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space š¯”¼ Ļ‰ . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on š¯”¼ Ļ‰ , and the solvability of the equation A u = v where A is a linear operator on š¯”¼ Ļ‰ .

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We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space š¯”¼ Ļ‰ . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on š¯”¼ Ļ‰ , and the solvability of the equation A u = v where A is a linear operator on š¯”¼ Ļ‰ .

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Available abstract

We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space š¯”¼ Ļ‰ . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on š¯”¼ Ļ‰ , and the solvability of the equation A u = v where A is a linear operator on š¯”¼ Ļ‰ .

Key concepts: Hilbert space, Von Neumann's theorem, Mathematics, Unbounded operator, Linear operators, Linear map, Diagonal, Operator (biology)

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