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Factorizations of EP Banach space operators and EP Banach algebra elements  [PDF]
Enrico Boasso
Mathematics , 2013,
Abstract: EP Banach space operators and EP Banach algebra elements are characterized using different kinds of factorizations. The results obtained generalize well-known characterizations of EP matrices, EP Hilbert space operators and EP $C^*$-algebra elements. Furthermore, new results that hold in these contexts are presented.
Factorizations of weighted EP Banach space operators and Banach algebra elements  [PDF]
Enrico Boasso,Dragan S. Djordjevic,Dijana Mosic
Mathematics , 2015,
Abstract: Weighted EP Banach space operators and Banach algebra elements are characterized using different kinds of factorizations. The results presented extend well-known characterizations of (weighted) EP matrices, (weighted) EP Hilbert space operators and (weighted) EP $C^*$-algebra elements.
Characterizations of EP and normal Banach algebra elements and Banach space operators  [PDF]
Enrico Boasso,Vladimir Rako?evi?
Mathematics , 2013,
Abstract: Several characterizations of EP and normal Moore-Penrose invertible Banach algebra elements will be considered. The Banach space operator case will be also studied. The results of the present article will extend well known facts obtained in the frames of matrices and Hilbert space operators.
Integral operators on the section space of a Banach bundle  [cached]
J. W. kitchen,D. A. Robbins
International Journal of Mathematics and Mathematical Sciences , 1993, DOI: 10.1155/s0161171293000560
Abstract: Let €:E ¢ ’X and :F ¢ ’X be bundles of Banach spaces, where X is a compact Hausdorff space, and let V be a Banach space. Let “( €) denote the space of sections of the bundle €. We obtain two representations of integral operators T: “( €) ¢ ’V in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral operators T: “( €) ¢ ’ “( ) which are C(X)-linear.
Drazin spectra of Banach space operators and Banach algebra elements  [PDF]
Enrico Boasso
Mathematics , 2013,
Abstract: Given a Banach Algebra $A$ and $a\in A$, several relations among the Drazin spectrum of $a$ and the Drazin spectra of the multiplication operators $L_a$ and $R_a$ will be stated. The Banach space operator case will be also examined. Furthermore, a characterization of the Drazin spectrum will be considered.
Some special characterisations of Fredholm operators in Banach space  [PDF]
Mahendra Shahi
BIBECHANA , 2014, DOI: 10.3126/bibechana.v11i0.10399
Abstract: A bounded linear operator which has a finite index and which is defined on a Banach space is often referred to in the literature as a Fredholm operator. Fredholm operators are important for a variety of reasons, one being the role that their index plays in global analysis. The aim of this paper is to prove the spectral theorem for compact operators in refined form and to describe some properties of the essential spectrum of general bounded operators by the use of the theorem of Fredholm operators. For this, we have analysed the Fredholm operator which is defined in a Banach space for some special characterisations.
A reflexive Banach space whose algebra of operators is not a Grothendieck space  [PDF]
Tomasz Kania
Mathematics , 2012, DOI: 10.1016/j.jmaa.2012.12.017
Abstract: By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive space $(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_p}$ ($p\in (1,\infty))$, thus giving a negative answer to the problem posed in the monograph of Diestel and Uhl which asks whether the space of operators on a reflexive Banach space is Grothendieck.
Existence of zeros for operators taking their values in the dual of a Banach space  [cached]
Ricceri Biagio
Fixed Point Theory and Applications , 2004,
Abstract: Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
Existence of zeros for operators taking their values in the dual of a Banach space
Biagio Ricceri
Fixed Point Theory and Applications , 2004, DOI: 10.1155/s1687182004310028
Abstract: Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
Strong convergence of an iterative sequence for maximal monotone operators in a Banach space  [PDF]
Fumiaki Kohsaka,Wataru Takahashi
Abstract and Applied Analysis , 2004, DOI: 10.1155/s1085337504309036
Abstract: We first introduce a modified proximal point algorithm formaximal monotone operators in a Banach space. Next, we obtain astrong convergence theorem for resolvents of maximal monotoneoperators in a Banach space which generalizes the previous resultby Kamimura and Takahashi in a Hilbert space. Using this result,we deal with the convex minimization problem and the variationalinequality problem in a Banach space.
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