Reducibility of operator semigroups and values of vector states

Reducibility of operator semigroups and values of vector states Let $$\mathcal S$$ S be a multiplicative semigroup of bounded linear operators on a complex Hilbert space $$\mathcal H$$ H , and let $$\Omega $$ Ω be the range of a vector state on $$\mathcal S$$ S so that $$\Omega = \{ \langle S \xi , \xi \rangle \,{:}\,S \in \mathcal S\}$$ Ω = { ⟨ S ξ , ξ ⟩ : S ∈ S } for some fixed unit vector $$\xi \in \mathcal H$$ ξ ∈ H . We study the structure of sets $$\Omega $$ Ω of cardinality two coming from irreducible semigroups $$\mathcal S$$ S . This leads us to sufficient conditions for reducibility and, in some cases, for the existence of common fixed points for $$\mathcal S$$ S . This is made possible by a thorough investigation of the structure of maximal families $$\mathcal F$$ F of unit vectors in $$\mathcal H$$ H with the property that there exists a fixed constant $$\rho \in \mathbb C$$ ρ ∈ C for which $$\langle x, y \rangle = \rho $$ ⟨ x , y ⟩ = ρ for all distinct pairs x and y in $$\mathcal F$$ F . Semigroup Forum Springer Journals

Reducibility of operator semigroups and values of vector states

Loading next page...
Springer US
Copyright © 2017 by Springer Science+Business Media New York
Mathematics; Algebra
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial