Trying some basic jQuery and JavaScript here.
The .width() gives me an integer value.  The .css('min-width') gives me a value ending in px.  Therefore I can't do math on this as is.  What is the recommended work around?
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').width());
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').css('min-width'));
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').width() >= $('#<%=lstProcessName.ClientID%>').parent('.column4').css('min-width'));
if ($('#<%=lstProcessName.ClientID%>').parent('.column4').width() >= $('#<%=lstProcessName.ClientID%>').parent('.column4').css('min-width')) {
  ...
}
                Use replace():
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').css('min-width').replace('px', ''));
Alternatively, you could use the parseInt function:
alert(parseInt('1px')); //Result: 1
                        The better way is to use parseInt. jQuery functions .width() and .height() work quite so.
Also, it would be good to encapsulate fetching of this values in standalone functions:
.minHeight(), .minHeight( size ), .minHeight( function() )
.maxHeight(), ...
.minWidth(), ...
.maxWidth(), ...
Like this:
(function($, undefined) {
    var oldPlugins = {};
    $.each([ "min", "max" ], function(_, name) {
        $.each([ "Width", "Height" ], function(_, dimension) {
            var type = name + dimension,
                cssProperty = [name, dimension.toLowerCase()].join('-');
            oldPlugins[ type ] = $.fn[ type ];
            $.fn[ type ] = function(size) {
                var elem = this[0];
                if (!elem) {
                    return !size ? null : this;
                }
                if ($.isFunction(size)) {
                    return this.each(function(i) {
                        var $self = $(this);
                        $self[ type ](size.call(this, i, $self[ type ]()));
                    });
                }
                if (size === undefined) {
                    var orig = $.css(elem, cssProperty),
                        ret = parseFloat(orig);
                    return jQuery.isNaN(ret) ? orig : ret;
                } else {
                    return this.css(cssProperty, typeof size === "string" ? size : size + "px");
                }
            };
        });
    });
})(jQuery);
And your code will turn to:
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').width());
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').minWidth());
alert($('#<%=lstProcessName.ClientID%>').parent('.column4').width() >= $('#<%=lstProcessName.ClientID%>').parent('.column4').minWidth());
if ($('#<%=lstProcessName.ClientID%>').parent('.column4').width() >= $('#<%=lstProcessName.ClientID%>').parent('.column4').minWidth()) {
                        Some string manipulation to remove 'px' and then use parseInt to get it as a number:
var minWidth = parseInt($('#<%=lstProcessName.ClientID%>').parent('.column4').css('min-width').replace('px', ''), 10)
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