<abstract xmlns="http://www.w3.org/1999/xhtml">

For given unit vectors x1, · · ·, xn of a real Banach space E, we define
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2022-0008_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mrow><mi>ℒ</mi><mrow><mo>(</mo><mrow><msup><mrow></mrow><mi>n</mi></msup><mi>E</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><msub><mrow><mi>x</mi></mrow><mn>1</mn></msub><mo>,</mo><mo>…</mo><msub><mrow><mi>x</mi></mrow><mi>n</mi></msub></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo> <mrow><mi>T</mi><mo>∈</mo><mi>ℒ</mi><mrow><mo>(</mo><mrow><msup><mrow></mrow><mi>n</mi></msup><mi>E</mi></mrow><mo>)</mo></mrow><mo>:</mo><mrow><mo>|</mo> <mrow><mi>T</mi><mrow><mo>(</mo><mrow><msub><mrow><mi>x</mi></mrow><mn>1</mn></msub><mo>,</mo><mo>…</mo><msub><mrow><mi>x</mi></mrow><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow> <mo>|</mo></mrow><mo>=</mo><mrow><mo>‖</mo> <mi>T</mi> <mo>‖</mo></mrow><mo>=</mo><mn>1</mn></mrow> <mo>}</mo></mrow><mo>,</mo></mrow></math>
<tex-math>NA\left( {\mathcal{L}\left( {^nE} \right)} \right)\left( {{x_1}, \ldots {x_n}} \right) = \left\{ {T \in \mathcal{L}\left( {^nE} \right):\left| {T\left( {{x_1}, \ldots {x_n}} \right)} \right| = \left\| T \right\| = 1} \right\},</tex-math>
</alternatives>
</disp-formula>
where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|.
In this paper, we classify NA(ℒ(2l12))((x1, x2), (y1, y2)) for unit vectors (x1, x2), (y1, y2)∈ l12, where l12 = ℝ2 with the l1-norm.
</abstract>

For given unit vectors x1, · · ·, xn of a real Banach space E, we define



NA(ℒ(nE))(x1,…xn)={ T∈ℒ(nE):| T(x1,…xn) |=‖ T ‖=1 },
NA\left( {\mathcal{L}\left( {^nE} \right)} \right)\left( {{x_1}, \ldots {x_n}} \right) = \left\{ {T \in \mathcal{L}\left( {^nE} \right):\left| {T\left( {{x_1}, \ldots {x_n}} \right)} \right| = \left\| T \right\| = 1} \right\},


where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|.
In this paper, we classify NA(ℒ(2l12))((x1, x2), (y1, y2)) for unit vectors (x1, x2), (y1, y2)∈ l12, where l12 = ℝ2 with the l1-norm.

Norm attaining bilinear forms on the plane with the <italic>l</italic>1-norm

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Norm attaining bilinear forms on the plane with the -norm

For given unit vectors x1, · · ·, xn of a real Banach space E, we define



NA(ℒ(nE))(x1,…xn)={ T∈ℒ(nE):| T(x1,…xn) |=‖ T ‖=1 },
NA\left( {\mathcal{L}\left(...

Norm attaining bilinear forms on the plane with the l₁-norm

Pubblicato online: 18 nov 2022

Pagine: 115 - 124

Ricevuto: 31 mag 2021

DOI: https://doi.org/10.2478/ausm-2022-0008

Parole chiave
norm attaining bilinear forms

© 2022 Sung Guen Kim, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Norm attaining bilinear forms on the plane with the l1-norm

Pubblicato online: 18 nov 2022

Pagine: 115 - 124

Ricevuto: 31 mag 2021

DOI: https://doi.org/10.2478/ausm-2022-0008

Parole chiavenorm attaining bilinear forms

© 2022 Sung Guen Kim, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Norm attaining bilinear forms on the plane with the l₁-norm

Parole chiave
norm attaining bilinear forms