KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2007 / Cilt: 31 - Sayı: 4

Induced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C*-Algebra C(X)

Ahmed S. AL-RAWASHDEH
Ahmed Al-Rawashdeh
Wasfi Shatanawi
Sayfa
439–451
Yayın Tarihi
2007-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:For a compact space X, any group automorphism j of C(X,S1) induces a mapping Q on the Boolean algebra of the clopen subsets of X.
📊
Temel Bulgular & Veri:We prove that the disjointness of Q equivalent to qj is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when j(-1)=-1.
💡
Sonuç & Katkı:If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Unitary · Projections · Almost Isomorphisms

Özet

For a compact space X, any group automorphism j of C(X,S1) induces a mapping Q on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Q equivalent to qj is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when j(-1)=-1. Indeed, Q is a Boolean isomorphism iff qj preserves the product of projections. If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).

Abstract

For a compact space X, any group automorphism j of C(X,S1) induces a mapping Q on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Q equivalent to qj is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when j(-1)=-1. Indeed, Q is a Boolean isomorphism iff qj preserves the product of projections. If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).

🔖

Bu Makaleye Atıf Yap

AL-RAWASHDEH, A. S., Al-Rawashdeh, A., Shatanawi, W. (2007). Induced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C*-Algebra C(X). Turkish Journal of Mathematics, Cilt: 31 - Sayı: 4, 439–451. https://ajindex.com/articles/723388

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (1)

  1. 1] Al-Rawashdeh, A.: The Unitary Group As An Invariant of a Simple Unital C∗−Algebra, Ph.D Thesis, University of Ottawa, Canada (2003). [2] Al-Rawashdeh, A., Giordano, T., Booth, A.: Unitary Groups As a Complete Invariant, to appear. [3] Booth, A.: The Unitary Groups As a Complete Invariant for Simple Unital AF Algebras, Master Thesis, University of Ottawa (1998). [4] Davidson, K.R.: C∗−Algebras by Example, Fields Institute Monographs, 6, Amer. Math. Soc., Providencs, RI (1996) [5] Dye, H.: On the Geometry of Projections in Certain Operator Algebras, Ann. of Math., Second Series, 61, 73-89 (1955). [6] Halmos, P.R.: Lectures On Boolean Algrbras, Springer (1974). [7] de la Harpe, P., Jones, V.F.R.: An Introduction to C∗−Algebras, Universit´e de Gen`eve (1995). [8] Stone, M.: The Theory of Representations For Boolean Algebras, Trans. Amer. Math. Soc. 4, 37-111 (1936).