Substochastic operators in symmetric spaces

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Abstract First, we solve a crucial problem under which conditions increasing uniform ‐monotonicity is equivalent to lower local uniform ‐monotonicity. Next, we investigate properties of substochastic operators on with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using ‐monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space under addition assumption on . In our final discussion, we focus on compactness of admissible operators for Banach couples under additional assumption.