Guys, it's Deep Ellum and it's pronounced Ellum, just like it looks. I am from Dallas and can tell you some other history (from the Dallas Historical Society web page):

During the 1920s and 1930s, Dallas was known as "one of the hottest cities in the South." That is, in terms of the music that was playing. Deep Ellum, located just east of downtown, became "the" place to hear the great blues and jazz musicians of the time. Such notable artists as Blind Lemon Jefferson, Huddie "Leadbelly" Ledbetter, Texas Bill Day, Lonnie Johnson, Little Hat Jones, Emma Wright, Bessie Smith, Ma Rainey, and Benny Moten were regular entertainers in the area. According to pianist Sam Price, Deep Ellum was "a breeding ground, a place where musicians started out, and when they were good enough they left, went on to Kansas City and New York. In Deep Ellum there were more blues singers than just about anywhere else."

A popular song of the time, "Deep Ellum Blues" by Texas Bill Day, illustrated the night life of Deep Ellum.

    Ellum Street's paved in brass,
    Main Street's paved in gold. (repeat)
    I've got a good girl lives on East Commerce
    I wouldn't mistreat to save nobody's Soul.
    These Ellum Street women, Billiken,
    Do not mean you no good. (repeat)
    If you want to make a good women,
    Have to get on Haskell Avenue.

By the end of the 1930s and into the 1940s, Deep Ellum became increasingly dangerous and rough. The railroad that ran through on Elm and Central was torn up, making room for the Central Expressway. These changes contributed to the decline of the area and the change of the musical atmosphere.

And here are some other lyrics I found, where it is spelled the way we spell it here in Dallas:

DEEP ELLUM BLUES (DEEP ELM)
(Shelton Brothers)
HANK THOMPSON (CAPITOL, 1958)

You go down in Deep Ellum
Just to have a little fun
Better have your fifteen dollars
When that policeman comes
Oh, sweet mama
Papa's got them deep ellum blues
Oh, sweet mama
Papa's got them deep ellum blues

Now, once I knew a preacher
Preached the bible through and through
He went down in Deep Ellum
Now his preachin' days are through
Oh, sweet mama
Papa's got them deep ellum blues
Oh, sweet mama
Papa's got them deep ellum blues

You go down in Deep Ellum
Keep your money in your pants
Them red heads in Deep Ellum
They don't give a man a chance
Oh, sweet mama
Papa's got them deep ellum blues
Oh, sweet mama
Papa's got them deep ellum blues

You go down in Deep Ellum
Keep your money in your shoes
Them gals down in Deep Ellum
Got them Deep Ellum blues
Oh, sweet mama
Papa's got them deep ellum blues
Oh, sweet mama
Papa's got them deep ellum blues