Normed Linear Spaces Suppose that ε and F are normed linear spaces and ε ≠ 0. Prove that ℓ ( ε, F ) is complete, then is complete.

Functional Analysis Normed Linear Space Suppose that ε and F are normed linear spaces and ε ≠ 0. Prove that ℓ ( ε, F ) is complete, then F is complete.

Disease Data - Rectangular Coordinate system

1985 1990 1995 2000 Heart Disease 778375 727206 737,563 710760 Cancer 459121 510426 538,455 1220100 AIDS 1700 25370 43115 14999 I do not understand how to plot data. I need to do this for each disease as points in a rectangular coordinate system. Since I don't understand the first I cannot use a smooth line. Can the graphs constructed be classified as functions? Explain. I don't understand why is it reasonable that negative numbers are excluded from both the domain and the range of each of the disease graphs? What would the real-world i... click for more

Weak Convergence

Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.

Continuity of a linear functional on a topology.

Suppose that E is a vector space, L is a family of linear functionals on E , and g is a linear functional on E. Let t be the topology on E induced by L. Prove that g is t-continuous on E if and only if g is a linear combination of L.

Suppose that ε is a normed linear space. Let j: ε → ε** be the canonical imbedding and let x** be a linear functional on ε*. Then x** is weak* continuous if and only if x** Є j(ε).

Topology Suppose that ε is a normed linear space. Let j: ε → ε** be the canonical imbedding and let x** be a linear functional on ε*. Then x** is weak* continuous if and only if x** Є j(ε). See the attached file.