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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2017.1
- 수록면
- 623 - 630 (8page)
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For any nonzero elements $x,y$ in a normed space $X$, the angular and skew-angular distance is respectively defined by $\alpha[x,y]=\left\| \frac{x}{\|x\|}-\frac{y}{\|y\|}\right\|$ and $\beta[x,y]=\left\| \frac{x}{\|y\|}-\frac{y}{\|x\|}\right\|$. Also inequality $\alpha\leq \beta$ characterizes inner product spaces. Operator version of $\alpha$ has been studied by Pe\v{c}ari\'{c}, Raji\'{c}, and Saito, Tominaga, and Zou et al.\\In this paper, we study the operator version of $\beta$ by using Douglas' lemma. We also prove that the operator version of inequality $\alpha\leq \beta$ holds for commutating normal operators. Some examples are presented to show essentiality of these conditions.
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참고문헌 (9)
참고문헌 신청
C. F. Dunkl / 1964 / A simple norm inequality / Amer. Math. Monthly 71 : 53 ~ 54
H. Dehghan / 2013 / A characterization of inner product spaces related to the skew-angular distance / Math. Notes 93 (4) : 556 ~ 560
J. A. Clarkson / 1936 / Uniformly convex spaces / Trans. Amer. Math. Soc. 40 : 396 ~ 414
J. L. Massera / 1958 / Linear differential equations and functional analysis. I / Ann. of Math. 67 : 517 ~ 573
J. Pecaric / 2010 / Inequalities of the Dunkl-Williams type for absolute value operators / J. Math. Inequal. 4 : 1 ~ 10
H. Dehghan / 2013 / A characterization of inner product spaces related to the skew-angular distance / Math. Notes 93 (4) : 556 ~ 560
J. A. Clarkson / 1936 / Uniformly convex spaces / Trans. Amer. Math. Soc. 40 : 396 ~ 414
J. L. Massera / 1958 / Linear differential equations and functional analysis. I / Ann. of Math. 67 : 517 ~ 573
J. Pecaric / 2010 / Inequalities of the Dunkl-Williams type for absolute value operators / J. Math. Inequal. 4 : 1 ~ 10
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