### Abstract

In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].

Original language | English |
---|---|

Pages (from-to) | 135-143 |

Number of pages | 9 |

Journal | Publications de l institut mathematique-Beograd |

Volume | 90 |

Issue number | 104 |

DOIs | |

Publication status | Published - 2011 |

### Keywords

- nema

### Cite this

*Publications de l institut mathematique-Beograd*,

*90*(104), 135-143. https://doi.org/10.2298/PIM1104135S

**2-normed algebras-II.** / Srivastava, Neeraj; Bhattacharya, S.; Lal, S. N.

Research output: Contribution to journal › Article

*Publications de l institut mathematique-Beograd*, vol. 90, no. 104, pp. 135-143. https://doi.org/10.2298/PIM1104135S

}

TY - JOUR

T1 - 2-normed algebras-II

AU - Srivastava, Neeraj

AU - Bhattacharya, S.

AU - Lal, S. N.

PY - 2011

Y1 - 2011

N2 - In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].

AB - In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].

KW - nema

U2 - 10.2298/PIM1104135S

DO - 10.2298/PIM1104135S

M3 - Article

VL - 90

SP - 135

EP - 143

JO - Publications de l institut mathematique-Beograd

JF - Publications de l institut mathematique-Beograd

SN - 0350-1302

IS - 104

ER -