日時：2025年9月1日(月)～9月5日(金)下記参照
場所：立命館大学 びわこくさつキャンパス ウェストウィング6階 談話会室
講師：Lajos Molnar教授 (University of Szeged）
9月１日（月）
- Lajos Molnar (University of Szeged)：9:00-12:20
- Lajos Molnar (University of Szeged)：13:30-15:05
関数解析研究会（1日目）
- 水口洋康（立命館大学)：15:30-16:10
- Title: On the constants related to triangles inscribed to a half of the unit sphere of normed spaces
- Abstract:
To investigate the geometric structure of normed spaces, he geometric constants play important roles.
There exist a lot of geometric constants, and among them we treat constants related to arithmetic mean of the norms of x+y and x-y where x and y belong to the unit sphere of normed spaces.
- 安齋 真由（新潟大学)：16:20-17:00
- Title: The linear preserver problem for C-symmetric operators
- Abstract: TBA:
9月2日（火）
- Lajos Molnar (University of Szeged）：9:00-12:20
- Lajos Molnar (University of Szeged）：13:30-15:05
関数解析研究会（2日目）
- 羽鳥理（新潟大学）：15:30-16:10
- Title: POWER BOUNDED ELEMENTS IN BANACH ALGEBRAS
- Abstract:
Let B be a unital Banach algebra. An element x ∈
B which satisfies supn∈N ∥x
n∥ < ∞ is called power bounded. If
moreover x is invertible in B, and if supn∈Z ∥x
n∥ < ∞, then x
is called doubly power bounded. Doubly power bounded elements
appeared in a classical and seminal theorem of Gelfand [2].
Theorem 1. Suppose that a is a doubly power bounded element in
a unital Banach algebra B. If σ(a) = {1}, then a is the unit of B.
A celebrated theorem of Sz.-Nagy [1] states that a Hilbert space
operator is doubly power bounded if and only if it is similar to
a unitary operator. The structures of power bounded elements
in Fourier or Fourier-Stieltjes algebras were studied by Kanius and
Ulger [3]. Schreiber [4] has studied the commutative case. Let ¨ U =
{u ∈ B−1
: ∥u∥ = ∥u
−1∥ = 1}, DP B = {u ∈ B : u is doubly power bounded in B},
S1 = {u ∈ B : σ(u) ⊂ T
- Lajos Molnar (University of Szeged）：16:20-17:00
- Title: Isomorphisms of positive cones in operator algebras with respect to geometric means
- Abstract:
In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we extend our existing result from the case of von Neumann
9月3日（水）
- Lajos Molnar (University of Szeged）：9:00-12:20
- Lajos Molnar (University of Szeged）：13:30-15:05
9月4日（木）
- Lajos Molnar (University of Szeged）：9:00-12:20
- Lajos Molnar (University of Szeged）：13:30-15:05
9月5日（金）
- Lajos Molnar (University of Szeged）：9:00-12:20
日本語
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