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F. Bonsall (1954)
A Minimal Property of the Norm in Some Banach AlgebrasJournal of The London Mathematical Society-second Series
Á. Palacios (1988)
Jordan axioms for C * -algebrasManuscripta Mathematica, 61
K. Goodearl (1982)
Notes on real and complex C[*]-algebras
W. Kaup (1983)
A Riemann mapping theorem for bounded symmetric domains in complex Banach spacesMathematische Zeitschrift, 183
R. Schafer (1966)
An Introduction to Nonassociative Algebras
K. Mccrimmon (1966)
Structure and representations of noncommutative Jordan algebrasTransactions of the American Mathematical Society, 121
R. Braun, W. Kaup, H. Upmeier (1978)
A holomorphic characterization of JordanC*-algebrasMathematische Zeitschrift, 161
N. Jacobson (1956)
Structure of rings
N. Kalton (1974)
Spaces of compact operatorsMathematische Annalen, 208
(1957)
Sur certains theoremes de J
A. López, Á. Palacios (1986)
Primitive noncommutative Jordan algebras with nonzero socle, 96
J. Isidro, Á. Palacios (1996)
On the definition of real *-algebras, 124
Kaidi Amin, A. Campoy, Á. Palacios (2001)
Non associative C*-algebras revisitedNorth-holland Mathematics Studies, 189
R. Payá-Albert, J. Perez-Gonzalez, A. Rodríguez-Palacios (1984)
Type I Factor Representations of Non‐Commutative JB*‐AlgebrasProceedings of The London Mathematical Society
F. Bonsall, J. Duncan (1973)
Complete Normed Algebras
(2003)
Maximal algebra norms
T. Palmer (1994)
Banach algebras and the general theory of *-algebras
M. Youngson (1981)
Non-unital Banach Jordan algebras and C*-triple systemsProceedings of the Edinburgh Mathematical Society, 24
T. Lam (2002)
A first course in noncommutative rings
M. Cabrera, J. Martínez, A. Rodriguez (1992)
Structurable H∗-algebrasJournal of Algebra, 147
L. Hogben, K. Mccrimmon (1981)
Maximal modular inner ideals and the Jacobson radical of a Jordan algebraJournal of Algebra, 68
J. Guerrero, A. Rodríguez-Palacios, G. Wood (2003)
Banach Spaces Whose Algebras of Operators are Unitary: A Holomorphic ApproachBulletin of the London Mathematical Society, 35
J. Guerrero, Á. Palacios (1999)
The Geometry of Convex Transitive Banach SpacesBulletin of The London Mathematical Society, 31
J. Perez, L. Rico, A. Rodriguez (1994)
Full subalgebras of Jordan-Banach algebras and algebra norms on *-algebras, 121
N. Jacobson (1968)
Structure and Representations of Jordan Algebras
Julio Guerrero, A. Rodríguez-Palacios (2009)
Relatively weakly open sets in closed balls of Banach spaces, and the centralizerMathematische Zeitschrift, 262
J. Becerra-Guerrero, Miguel Martín (2004)
The Daugavet property of C ∗ -algebras, JB ∗ -triples, and of their isometric predualsJournal of Functional Analysis, 224
J. Martínez, A. Peralta (2000)
Separate weak*-continuity of the triple product in dual real JB*-triplesMathematische Zeitschrift, 234
Á. Palacios (1994)
Absolute Valued Algebras of Degree Two
J. Guerrero, Ginés Pérez, A. Peralta, A. Rodríguez-Palacios (2004)
Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rankMathematische Annalen, 330
H. Dales (2000)
Banach algebras and automatic continuity
J. Guerrero, A. Rodríguez-Palacios (2005)
Big points in C*-algebras and JB*-triplesQuarterly Journal of Mathematics, 56
Kaidi Amin, A. Campoy, Á. Palacios (2001)
A holomorphic characterization¶of C*- and JB*-algebrasmanuscripta mathematica, 104
S. Cleveland (1963)
Homomorphisms of non-commutative ∗-algebrasPacific Journal of Mathematics, 13
Á. Palacios (1990)
Automatic continuity with application to C*-algebrasMathematical Proceedings of the Cambridge Philosophical Society, 107
J. Wright, M. Youngson (1977)
A Russo Dye Theorem for Jordan C*-AlgehrasNorth-holland Mathematics Studies, 27
K. Mccrimmon (1971)
Noncommutative Jordan ringsTransactions of the American Mathematical Society, 158
K. Zhevlakov (1982)
Rings that are nearly associative
W. Kaup (1975)
Über die Automorphismen Graßmannscher Mannigfaltigkeiten unendlicher DimensionMathematische Zeitschrift, 144
B. Aupetit (1979)
Propriétés spectrales des algèbres de Banach
C. Rickart (1974)
General Theory of Banach Algebras
J. Guerrero, S. Cowell, Á. Palacios, G. Wood (2004)
Unitary Banach algebrasStudia Mathematica, 162
M. Hansen, R. Kadison (1996)
Banach algebras with unitary norms.Pacific Journal of Mathematics, 175
Á. Palacios (1980)
A Vidav–Palmer Theorem for Jordan C*-Algebras and Related TopicsJournal of The London Mathematical Society-second Series
A. Peralta, L. Stachó (2001)
Atomic decomposition of real JBW‐triplesQuarterly Journal of Mathematics, 52
R. Payá, J. Pérez, Angel Rodriguez (1982)
Noncommutative Jordan C*-algebrasmanuscripta mathematica, 37
S. Kakutani, G. Mackey (1944)
Two Characterizations of Real Hilbert SpaceAnnals of Mathematics, 45
E. Cowie (1983)
An analytic characterization of groups with no finite conjugacy classes, 87
J. Isidro, W. Kaup, Á. Palacios (1995)
On real forms of JB*-triplesmanuscripta mathematica, 86
Á. Palacios (1991)
An approach to Jordan-Banach algebras from the theory of nonassociative complete normed algebras, 97
S. Rolewicz (1985)
Metric Linear Spaces
M. Navarro (1998)
Some Characterizations of Finite-Dimensional Hilbert SpacesJournal of Mathematical Analysis and Applications, 223
Á. Palacios, J. Guerrero (2000)
Transitivity of the norm on Banach spaces having a Jordan structureManuscripta Mathematica, 101
AbstractWe study unitary Banach algebras, as defined by M. L. Hansen and R. V. Kadison in 1996, as well as some related concepts like maximal or uniquely maximal Banach algebras. We show that a norm-unital Banach algebra is uniquely maximal if and only if it is unitary and has minimality of the equivalent norm. We prove that every unitary semisimple commutative complex Banach algebra has a conjugate-linear involution mapping each unitary element to its inverse, and that, endowed with such an involution, becomes a hermitian -algebra. The possibility of removing the requirement of commutativity in the above statement is also considered. The paper concludes by translating to real algebras some results previously known in the complex case. In particular, we show that every maximal semisimple finite-dimensional real Banach algebra is isometrically isomorphic to a real C-algebra.
The Quarterly Journal of Mathematics – Oxford University Press
Published: Jun 18, 2007
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