JV-algebras

1980 ◽  
Vol 87 (1) ◽  
pp. 47-50 ◽  
Author(s):  
J. Martinez Moreno
Keyword(s):  
Banach Space ◽  
Jordan Algebra ◽  
Complex Banach Space ◽  
C Algebra ◽  
Image Position

Let J be a complex Banach space and a complex Jordan algebra equipped with an algebra involution *. Then J is a Jordan C*-algebra if the following conditions are satisfied:(Ua is defined on page 3).

On the centres of hereditary JBW-subalgebras of a JBW-algebra

1979 ◽  
Vol 85 (2) ◽  
pp. 317-324 ◽  
Author(s):  
C. M. Edwards
Keyword(s):  
Banach Space ◽  
General Theory ◽  
Jordan Algebra ◽  
Identity Element ◽  
Image Position

A JB-algebra A is a real Jordan algebra, which is also a Banach space, the norm in which satisfies the conditions thatandfor all elements a and b in A. It follows from (1.1) and (l.2) thatfor all elements a and b in A. When the JB-algebra A possesses an identity element then A is said to be a unital JB-algebra and (1.2) is equivalent to the condition thatfor all elements a and b in A. For the general theory of JB-algebras the reader is referred to (2), (3), (7) and (10).

scholarly journals On compact action in JB-algebras

1983 ◽  
Vol 26 (3) ◽  
pp. 353-360 ◽  
Author(s):  
L. J. Bunce
Keyword(s):  
Banach Space ◽  
Jordan Algebra ◽  
Dual Space ◽  
Image Position

A real Jordan algebra which is also a Banach space with a norm which satisfiesfor each pair a, b of elements, is said to be a JB-algebra. A JB-algebra which is also a Banach dual space is said to be a JBW-algebra.

Growth conditions on subharmonic functions and resolvents of operators

1985 ◽  
Vol 97 (2) ◽  
pp. 321-324
Author(s):  
J. R. Partington
Keyword(s):  
Banach Space ◽  
Numerical Range ◽  
Bounded Operator ◽  
Complex Banach Space ◽  
Growth Conditions ◽  
Subharmonic Functions ◽  
Image Position

Let X be a complex Banach space and T a bounded operator on X. The numerical range of T is defined by

scholarly journals Expansion of analytic functions of an operator in series of Faber polynomials

1997 ◽  
Vol 56 (2) ◽  
pp. 303-318 ◽  
Author(s):  
Maurice Hasson
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Analytic Functions ◽  
Bounded Linear Operator ◽  
Complex Banach Space ◽  
Faber Polynomials ◽  
Bounded Linear ◽  
In Series ◽  
Image Position

Let T: B → B be a bounded linear operator on the complex Banach space B and let f(z) be analytic on a domain D containing the spectrum Sp(T) of T. Then f(T) is defined bywhere C is a contour surrounding SP(T) and contained in D.

scholarly journals GROWTH CONDITIONS FOR OPERATORS WITH SMALLEST SPECTRUM

2014 ◽  
Vol 57 (3) ◽  
pp. 665-680
Author(s):  
H. S. MUSTAFAYEV
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Growth Conditions ◽  
Invertible Operator ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Formula Group ◽  
Image Position

AbstractLet A be an invertible operator on a complex Banach space X. For a given α ≥ 0, we define the class $\mathcal{D}$Aα(ℤ) (resp. $\mathcal{D}$Aα (ℤ+)) of all bounded linear operators T on X for which there exists a constant CT>0, such that $ \begin{equation*} \Vert A^{n}TA^{-n}\Vert \leq C_{T}\left( 1+\left\vert n\right\vert \right) ^{\alpha }, \end{equation*} $ for all n ∈ ℤ (resp. n∈ ℤ+). We present a complete description of the class $\mathcal{D}$Aα (ℤ) in the case when the spectrum of A is real or is a singleton. If T ∈ $\mathcal{D}$A(ℤ) (=$\mathcal{D}$A0(ℤ)), some estimates for the norm of AT-TA are obtained. Some results for the class $\mathcal{D}$Aα (ℤ+) are also given.

Representations and Divisibility of Operator Polynomials

1978 ◽  
Vol 30 (5) ◽  
pp. 1045-1069 ◽  
Author(s):  
I. Gohberg ◽  
P. Lancaster ◽  
L. Rodman
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Complex Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Image Position

Let be a complex Banach space and the algebra of bounded linear operators on . In this paper we study functions from the complex numbers to of the form

An unbounded spectral mapping theorem

1968 ◽  
Vol 8 (1) ◽  
pp. 119-127 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Subset ◽  
Complex Banach Space ◽  
Complex Numbers ◽  
Spectral Mapping Theorem ◽  
Complex Polynomials ◽  
Spectral Mapping ◽  
Image Position ◽  
Densely Defined

Recall that the spectrum, σ(T), of a linear operator T in a complex Banach space is the set of complex numbers λ such that T—λI does not have a densely defined bounded inverse. It is known [7, § 5.1] that σ(T) is a closed subset of the complex plane C. If T is not bounded, σ(T) may be empty or the whole of C. If σ(T) ≠ C and T is closed the spectral mapping theorem, is valid for complex polynomials p(z) [7, §5.7]. Also, if T is closed and λ ∉ σ(T), (T–λI)−1 is everywhere defined.

scholarly journals Approximate point spectrum and commuting compact perturbations

1986 ◽  
Vol 28 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Vladimir Rakočević
Keyword(s):  
Banach Space ◽  
Essential Spectrum ◽  
Point Spectrum ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Complex Numbers ◽  
Approximate Point Spectrum ◽  
Infinite Dimensional ◽  
Compact Perturbations ◽  
Image Position

Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B (X) (K(X)). Let σ(A) and σa(A) denote, respectively, the spectrum and approximate point spectrum of an element A of B(X). Setσem(A)and σeb(A) are respectively Schechter's and Browder's essential spectrum of A ([16], [9]). σea (A) is a non-empty compact subset of the set of complex numbers ℂ and it is called the essential approximate point spectrum of A ([13], [14]). In this note we characterize σab(A) and show that if f is a function analytic in a neighborhood of σ(A), then σab(f(A)) = f(σab(A)). The relation between σa(A) and σeb(A), that is exhibited in this paper, resembles the relation between the σ(A) and the σeb(A), and it is reasonable to call σab(A) Browder's essential approximate point spectrum of A.

Complex strict and uniform convexity and hyponormal operators

1984 ◽  
Vol 96 (3) ◽  
pp. 483-493 ◽  
Author(s):  
Kirsti Mattila
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Numerical Range ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Uniform Convexity ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hyponormal Operators ◽  
Image Position

Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. The (spatial) numerical range of an operator TεB(X) is defined as the setIf V(T) ⊂ ℝ, then T is called hermitian. More about numerical ranges may be found in [8] and [9].

scholarly journals Hermitian Operators on Banach Jordan Algebras

1979 ◽  
Vol 22 (2) ◽  
pp. 169-180 ◽  
Author(s):  
M. A. Youngson
Keyword(s):  
Banach Space ◽  
Jordan Algebra ◽  
Numerical Range ◽  
Jordan Algebras ◽  
Image Position

In this note, we examine some of the properties of Hermitian operators on complex unital Banach Jordan algebras, that is, those operators with real numerical range. Recall that a unital Banach Jordan algebra J, is a (real or complex) Jordan algebra with product a ˚ b, having a unit 1, and a norm ∥·∥, such that J, with norm ∥·∥, is a Banach space, ∥1∥ = 1, and, for all a and b in j,

Sign in / Sign up

Export Citation Format

Share Document