On pexider type of Hilbert C$^* $-module higher derivations

Ekrami, Sayed Khalil

doi:10.22034/as.2025.20588.1671

On pexider type of Hilbert C $^{*}$ -module higher derivations

Document Type : Research Paper

Author

Sayed Khalil Ekrami

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

10.22034/as.2025.20588.1671

Abstract

In this paper, we introduce the concept of pexider Hilbert C

^{*}

-module higher

{A_{n}, B_{n}, D_{n}}

-derivations. Specifically, we focus on a Hilbert C

^{*}

-module

M

and provide a comprehensive characterization of these pexider Hilbert C

^{*}

-module higher

{A_{n}, B_{n}, D_{n}}

-derivations

{Φ_{n}}_{n = 0}^{\infty}

M

in relation to pexider Hilbert C

^{*}

-module

{α_{n}, β_{n}, δ_{n}}

-derivations

{φ_{n}}_{n = 1}^{\infty}

M

. We demonstrate that for every pexider Hilbert C

^{*}

-module higher

{A_{n}, B_{n}, D_{n}}

-derivation

{Φ_{n}}_{n = 0}^{\infty}

M

, there exists a unique sequence of pexider Hilbert C

^{*}

-module

{α_{n}, β_{n}, δ_{n}}

-derivations

{φ_{n}}_{n = 1}^{\infty}

M

such that

{\begin{array}{lr} φ_{n} = \sum_{k = 1}^{n} (\sum_{\sum_{j = 1}^{k} r_{j} = n} (- 1)^{k - 1} r_{1} Φ_{r_{1}} Φ_{r_{2}} \dots Φ_{r_{k}}), \\ α_{n} = \sum_{k = 1}^{n} (\sum_{\sum_{j = 1}^{k} r_{j} = n} (- 1)^{k - 1} r_{1} A_{r_{1}} A_{r_{2}} \dots A_{r_{k}}), \\ β_{n} = \sum_{k = 1}^{n} (\sum_{\sum_{j = 1}^{k} r_{j} = n} (- 1)^{k - 1} r_{1} B_{r_{1}} B_{r_{2}} \dots B_{r_{k}}), \\ δ_{n} = \sum_{k = 1}^{n} (\sum_{\sum_{j = 1}^{k} r_{j} = n} (- 1)^{k - 1} r_{1} D_{r_{1}} D_{r_{2}} \dots D_{r_{k}}), \end{array}

for all positive integers

n

, where the inner summation is taken over all positive integers

r_{j}

with

\sum_{j = 1}^{k} r_{j} = n

Keywords

References

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Algebraic Structures and Their Applications

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On pexider type of Hilbert C $^{*}$ -module higher derivations

References

Volume 12, Issue 2
May 2025
Pages 155-167

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On pexider type of Hilbert C∗-module higher derivations

References

Volume 12, Issue 2May 2025Pages 155-167

Files

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How to cite

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On pexider type of Hilbert C $^{*}$ -module higher derivations

Volume 12, Issue 2
May 2025
Pages 155-167