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Subspace Superconvex-Cyclicity on Infinite-Dimensional Banach Spaces | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 آذر 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.32489.1897 | ||
| نویسندگان | ||
| Negin Sharife؛ Meysam Asadipour* ؛ Rohollah Parvinianzadeh | ||
| Department of Mathematics, Yasouj University, Yasouj, Iran. | ||
| تاریخ دریافت: 02 مرداد 1405، تاریخ بازنگری: 06 شهریور 1405، تاریخ پذیرش: 09 شهریور 1405 | ||
| چکیده | ||
| Convex-cyclicity, superconvex-cyclicity, and subspace convex-cyclicity have been studied as three related ways of weakening or localizing orbit-density phenomena in linear dynamics. However, the corresponding subspace form of superconvex-cyclicity has not been isolated and examined as a separate notion. In this paper, we fill this gap by introducing subspace superconvex-cyclic operators on infinite-dimensional complex Banach spaces. The new notion requires the superconvex hull of an orbit to meet a prescribed closed subspace densely. We first place this class among its neighboring notions by proving that every subspace convex-cyclic operator is subspace superconvex-cyclic. We then show that this inclusion is strict and, at the same time, that subspace superconvex-cyclicity does not coincide with superconvex-cyclicity on the ambient space. A single explicit construction establishes both separations simultaneously. Finally, we prove an existence theorem showing that every superconvex-cyclic operator on a separable infinite-dimensional complex Banach space generates subspace superconvex-cyclic behavior on a suitable proper closed subspace. | ||
| کلیدواژهها | ||
| Superconvex-cyclicity؛ subspace convex-cyclicity؛ subspace superconvex-cyclic operators | ||
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