Page 616 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 616
ANALYSIS AND ITS APPLICATIONS
Cuntz–Pimsner algebras associated to finite rank vector bundles twisted
by a homeomorphism
Maria Stella Adamo, adamo@axp.mat.uniroma2.it
University of Leipzig, Germany and Università di Roma "La Sapienza", Italy
Coauthors: Dawn Archey, Magdalena Georgescu, Marzieh Forough, Ja A Jeong,
Karen Strung, Maria Grazia Viola
In this talk, we will discuss the structural properties of Cuntz-Pimsner algebras arising by the
continuous sections Γ(V, α) of a complex locally trivial vector bundle V on a compact Haus-
dorff space X twisted by a minimal homeomorphism α : X → X. We tackle this problem
by identifying "large enough" C*-subalgebras that capture the fundamental properties of the
containing Cuntz-Pimsner algebra but are more tractable. Lastly, we will examine conditions
when these C*-algebras can be classified using the Elliott invariant.
A glimpse to the Berezin numbers inequality
Mojtaba Bakherad, mojtaba.bakherad@yahoo.com
Faculty of Mathematics, University of Sistan and Baluchestan,
Zahedan, Islamic Republic of Iran
A reproducing kernel Hilbert space (RKHS for short) H = H(Ω) is a Hilbert space of complex
valued functions on a (nonempty) set Ω, which has the property that point evaluations are con-
tinuous i.e. for each λ ∈ Ω the map f → f (λ) is a continuous linear functional on H. The
Riesz representation theorem ensure that for each λ ∈ Ω there is a unique element kλ ∈ H such
that f (λ) = f, kλ , for all f ∈ H. The collection {kλ : λ ∈ Ω} is called the reproducing kernel
of H. If {en} is an orthonormal basis for a functional Hilbert space H, then the reproducing
n en(λ)en(z). For λ ∈ Ω, let kˆλ =
kernel of H is given by kλ(z) = kλ be the normalized
kλ
reproducing kernel of H. For a bounded linear operator A on H, the function A defined on Ω by
A(λ) = Akˆλ, kˆλ is the Berezin symbol of A, which firstly have been introduced by Berezin.
The Berezin set and the Berezin number of the operator A are defined by
Ber(A) := {A(λ) : λ ∈ Ω} and ber(A) := sup{|A(λ)| : λ ∈ Ω},
respectively. Namely, the Berezin transform has been investigated in detail for the Toeplitz
and Hankel operators on the Hardy and Bergman spaces; it is widely applied in the various
questions of analysis and uniquely determines the operator(i.e., for all λ ∈ Ω, A(λ) = B(λ)
implies A = B).
The objective of this paper is to present a generalized Berezin number inequality and refine
the new inequalities. We also present some results of Berezin number inequalities involving
f -connection of operators.
References
[1] M. BAKHERAD, Some Berezin number inequalities for operator matrices, Czechoslovak
Math. J. 68, 143 (2018), 997–1009.
[2] M. BAKHERAD, M. T. GARAYEV, Berezin number inequalities for operators, Concrete
Operators 6 (2019), 33–43.
614
Cuntz–Pimsner algebras associated to finite rank vector bundles twisted
by a homeomorphism
Maria Stella Adamo, adamo@axp.mat.uniroma2.it
University of Leipzig, Germany and Università di Roma "La Sapienza", Italy
Coauthors: Dawn Archey, Magdalena Georgescu, Marzieh Forough, Ja A Jeong,
Karen Strung, Maria Grazia Viola
In this talk, we will discuss the structural properties of Cuntz-Pimsner algebras arising by the
continuous sections Γ(V, α) of a complex locally trivial vector bundle V on a compact Haus-
dorff space X twisted by a minimal homeomorphism α : X → X. We tackle this problem
by identifying "large enough" C*-subalgebras that capture the fundamental properties of the
containing Cuntz-Pimsner algebra but are more tractable. Lastly, we will examine conditions
when these C*-algebras can be classified using the Elliott invariant.
A glimpse to the Berezin numbers inequality
Mojtaba Bakherad, mojtaba.bakherad@yahoo.com
Faculty of Mathematics, University of Sistan and Baluchestan,
Zahedan, Islamic Republic of Iran
A reproducing kernel Hilbert space (RKHS for short) H = H(Ω) is a Hilbert space of complex
valued functions on a (nonempty) set Ω, which has the property that point evaluations are con-
tinuous i.e. for each λ ∈ Ω the map f → f (λ) is a continuous linear functional on H. The
Riesz representation theorem ensure that for each λ ∈ Ω there is a unique element kλ ∈ H such
that f (λ) = f, kλ , for all f ∈ H. The collection {kλ : λ ∈ Ω} is called the reproducing kernel
of H. If {en} is an orthonormal basis for a functional Hilbert space H, then the reproducing
n en(λ)en(z). For λ ∈ Ω, let kˆλ =
kernel of H is given by kλ(z) = kλ be the normalized
kλ
reproducing kernel of H. For a bounded linear operator A on H, the function A defined on Ω by
A(λ) = Akˆλ, kˆλ is the Berezin symbol of A, which firstly have been introduced by Berezin.
The Berezin set and the Berezin number of the operator A are defined by
Ber(A) := {A(λ) : λ ∈ Ω} and ber(A) := sup{|A(λ)| : λ ∈ Ω},
respectively. Namely, the Berezin transform has been investigated in detail for the Toeplitz
and Hankel operators on the Hardy and Bergman spaces; it is widely applied in the various
questions of analysis and uniquely determines the operator(i.e., for all λ ∈ Ω, A(λ) = B(λ)
implies A = B).
The objective of this paper is to present a generalized Berezin number inequality and refine
the new inequalities. We also present some results of Berezin number inequalities involving
f -connection of operators.
References
[1] M. BAKHERAD, Some Berezin number inequalities for operator matrices, Czechoslovak
Math. J. 68, 143 (2018), 997–1009.
[2] M. BAKHERAD, M. T. GARAYEV, Berezin number inequalities for operators, Concrete
Operators 6 (2019), 33–43.
614
