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- W3208935534 abstract "We consider a Hilbert space that is a product of a finite number of Hilbert spaces and that are represented by operators acting on the Hilbert spaces that form the product space. We attribute operatorial properties to the componental rather than to the full operators. The operatorial properties that we discuss include nonexpansivity, firm non-expansivity, relaxed firm nonexpansivity, averagedness, being a cutter, quasi-nonexpansivity, strong quasi-nonexpansivity, strict quasi-nonexpansivity and contraction. Some relationships between whose componental have such properties and that have these properties on the product space are studied. This enables also to define componental fixed point sets and to study their properties. For componental contractions we offer a variant of the Banach fixed point theorem. Our motivation comes from the desire to extend a fully-simultaneous method that takes into account sparsity of the linear system in order to accelerate convergence [Censor et al., On diagonally relaxed orthogonal projection methods, SIAM J. Sci. Comput. 30 (2008), 473-504]. This was originally applicable to the linear case only and gives rise to an iterative process that uses dfferent componental during iterations." @default.
- W3208935534 created "2021-11-08" @default.
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- W3208935534 date "2021-11-29" @default.
- W3208935534 modified "2023-09-27" @default.
- W3208935534 title "On Componental Operators in Hilbert Space." @default.
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