Is there a faster way of splitting strings?

static string MemoryToLower(ReadOnlySpan<char> span)
{
    Span<char> chars = stackalloc char[span.Length];

    for (int i = 0; i < span.Length; i++)
    {
        char c = span[i];
        chars[i] = (c >= 'A' && c <= 'Z') ? (char)(c + 32) : c;
    }

    return new string(chars);
}

static SearchValues<char> searchValues = SearchValues.Create(new[] { ' ', '\r', '\n', ',', '.', '?', '"', '\'', ';', '!', '\t', '(', ')', '[', ']', '<', '>', '+', '-', '*' });

static List<string> Tokenizer(string input)
{
    var startIndex = 0;
    var list = new List<string>();

    for (var i = 0; i < input.Length; i++)
    {
        var c = input[i];
        if (searchValues.Contains(c))
        {
            if (i - startIndex > 0)
                list.Add(MemoryToLower(input.AsSpan(startIndex, i - startIndex)));
                
            startIndex = i + 1;
        }
    }
    if (input.Length - startIndex > 0)
        list.Add(MemoryToLower(input.AsSpan(startIndex, input.Length - startIndex)));
    
    return list;
}