Araştırma Makalesi
Yıl 2020,
Cilt: 49 Sayı: 5, 1798 - 1803, 06.10.2020
Öz
Kaynakça
- [1] O.M. Di Vincenzo, P. Koshlukov and R. La Scala, Involutions for upper triangular matrix algebras, Adv. in Appl. Math. 37, 541–568, 2006.
- [2] J. Dixmier, C*-Algebras, North-Holland, Amsterdam, 1977.
- [3] N. Jacobson, A topology for the set of primitive ideals in an arbitrary ring, Proc, Nat, Acad, Sci. U.S.A. 31, 333–338, 1945.
- [4] T.K. Lee and Y. Zhou, Armendariz and reduced rings, Comm. Algebra 32 (6), 2287– 2299, 2004.
- [5] G.J. Murphy, C*-Algebras and Operator Theory Academic Press, 1990.
- [6] T.W. Palmer, Banach Algebras and the General Theory of $\ast$-Algebras Volume I Al- gebras and Banach Algebras, Encyclopedia of Mathematics and its Applications, Vol. 1, 1994.
- [7] V. Paulsen, Completely Bounded Maps and Operator Algebras, vol. 78, Cambridge University Press, 2002.
Yıl 2020,
Cilt: 49 Sayı: 5, 1798 - 1803, 06.10.2020
Öz
In this paper we provide new examples of Banach $ \ast $-subalgebras of the matrix algebra $M_n(\mathscr{A}) $ over a commutative unital $C^*$-algebra $\mathscr{A}$. For any involutive algebra, we define two involutions on the triangular matrix extensions. We prove that the triangular matrix algebras over any commutative unital $C^*$-algebra are Banach ${\ast}$-algebras and that the primitive ideals of these algebras and some of their Banach $ \ast $-subalgebras are all maximal.
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Anahtar Kelimeler
Kaynakça
- [1] O.M. Di Vincenzo, P. Koshlukov and R. La Scala, Involutions for upper triangular matrix algebras, Adv. in Appl. Math. 37, 541–568, 2006.
- [2] J. Dixmier, C*-Algebras, North-Holland, Amsterdam, 1977.
- [3] N. Jacobson, A topology for the set of primitive ideals in an arbitrary ring, Proc, Nat, Acad, Sci. U.S.A. 31, 333–338, 1945.
- [4] T.K. Lee and Y. Zhou, Armendariz and reduced rings, Comm. Algebra 32 (6), 2287– 2299, 2004.
- [5] G.J. Murphy, C*-Algebras and Operator Theory Academic Press, 1990.
- [6] T.W. Palmer, Banach Algebras and the General Theory of $\ast$-Algebras Volume I Al- gebras and Banach Algebras, Encyclopedia of Mathematics and its Applications, Vol. 1, 1994.
- [7] V. Paulsen, Completely Bounded Maps and Operator Algebras, vol. 78, Cambridge University Press, 2002.
Toplam 7 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Ekim 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 5 |