PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
January 18, 2026Proceedings of the American Mathematical Society0 citations

Direct decomposition of 𝜌-contraction and the unitary 𝜌-dilation

View Full Paper
HGHwa-Long GauPWPy Wu

Key Points

  • This work aims to explore the characteristics of rho-contractions in Hilbert spaces and derive specific bounds.
  • Analysis of rho-contraction properties under various transformations.
  • Use of unit vectors to evaluate contraction behaviors.
  • Mathematical proofs to establish relationships between norms and parameters.
  • If certain norms are equal to a constant c, they must be less than or equal to certain thresholds.
  • Establishes that norms of A applied to unit vectors can be derived analytically based on rho and n.

Abstract

For ρ > 1 >1, let A A be a ρ -contraction on a Hilbert space H H. Letting n ≥ 1 n 1 and x x be a unit vector in H H, we show that (a) if ‖ A x ‖ = ‖ A 2 x ‖ = ⋯ = ‖ A n x ‖ ≡ c \|Ax\|=\|A²x\|= =\|Aⁿx\| c, then c ≤ ρ (ρ + n − 1) / n c (+n-1) /n, and (b) ‖ A x ‖ = ‖ A

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Gau et al. (2026) studied this question.

synapsesocial.com/papers/696c7835eb60fb80d1396643https://doi.org/10.1090/proc/17547
Ask AI
Helpful
Bookmark
Share
View Full Paper