Abstract: We introduce Schatten-class operators in p-adic Hilbert spaces and study their properties and give several examples. We also show that the Trace class operators in p-adic Hilbert spaces strictly contains the class of completely continuous operators.This gives a totally new perspective to the space of compact operators in p-adic Hilbert spaces. Apart from its intrinsic interest as discussed in this paper, p-adic functional analysis is a fast growing research area and has numerous applications in differential equations, statistics, quantum physics, dynamical systems, cognitive sciences, psychology and sociology, to name a few.

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